Search: monomials

Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (\left\(3x^{-2}y^{3}\right\)^{2}\cdot\left\(9x^{4}y^{-1}\right\)^{-1}) को \(cx^{r}y^{s}\) लिखा जाए, तो (c+r+s) का मान क्या है?

If (\left\(3x^{-2}y^{3}\right\)^{2}\cdot\left\(9x^{4}y^{-1}\right\)^{-1}) is written as \(cx^{r}y^{s}\), what is the value of (c+r+s)?

Explanation opens after your attempt

Correct Answer

B. (2)

Step 1

Concept

The expression is \(9x^{-4}y^{6}\cdot\frac{1}{9}x^{-4}y=x^{-8}y^{7}\). Thus (c=1), (r=-8), (s=7), and (c+r+s=0).

Step 2

Why this answer is correct

The correct answer is B. (2). The expression is \(9x^{-4}y^{6}\cdot\frac{1}{9}x^{-4}y=x^{-8}y^{7}\). Thus (c=1), (r=-8), (s=7), and (c+r+s=0).

Step 3

Exam Tip

अभिव्यक्ति \(9x^{-4}y^{6}\cdot\frac{1}{9}x^{-4}y=x^{-8}y^{7}\) है। इसलिए (c=1), (r=-8), (s=7), और (c+r+s=0) होता है।

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https://muftshiksha.com/question/if-left-3x-2-y-3-right-2-cdot-left-9x-4-y-1-right-1-is-written-as-cx-r-y-s-what-is-the-val

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
यदि (\left(3x^{-2}y^{3}\right)^{2}\cdot\left(9x^{4}y^{-1}\right)^{-1}) को (cx^{r}y^{s}) लिखा जाए, तो (c+r+s) का मान क्या है?

Question English:
If (\left(3x^{-2}y^{3}\right)^{2}\cdot\left(9x^{4}y^{-1}\right)^{-1}) is written as (cx^{r}y^{s}), what is the value of (c+r+s)?

Options:
A. (1)
B. (2)
C. (3)
D. (4)

Correct Answer:
B. (2)

Explanation Hindi:
अभिव्यक्ति (9x^{-4}y^{6}\cdot\frac{1}{9}x^{-4}y=x^{-8}y^{7}) है। इसलिए (c=1), (r=-8), (s=7), और (c+r+s=0) होता है।

Explanation English:
The expression is (9x^{-4}y^{6}\cdot\frac{1}{9}x^{-4}y=x^{-8}y^{7}). Thus (c=1), (r=-8), (s=7), and (c+r+s=0).

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{125x^{-9}}{64y^{12}}\right\)^{-\frac{1}{3}}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{125x^{-9}}{64y^{12}}\right\)^{-\frac{1}{3}})?

Explanation opens after your attempt

Correct Answer

A. \(\frac{4x^{3}y^{4}}{5}\)

Step 1

Concept

We get (\left\(\frac{125x^{-9}}{64y^{12}}\right\)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}}). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{4x^{3}y^{4}}{5}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{4x^{3}y^{4}}{5}\). We get (\left\(\frac{125x^{-9}}{64y^{12}}\right\)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}}). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{4x^{3}y^{4}}{5}\).

Step 3

Exam Tip

(\left\(\frac{125x^{-9}}{64y^{12}}\right\)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}})। \(-\frac{1}{3}\) घात लेने पर व्युत्क्रम \(\frac{4x^{3}y^{4}}{5}\) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
(\left(\frac{125x^{-9}}{64y^{12}}\right)^{-\frac{1}{3}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{125x^{-9}}{64y^{12}}\right)^{-\frac{1}{3}})?

Options:
A. (\frac{4x^{3}y^{4}}{5})
B. (\frac{5}{4x^{3}y^{4}})
C. (\frac{5x^{-3}}{4y^{4}})
D. (\frac{4y^{4}}{5x^{3}})

Correct Answer:
A. (\frac{4x^{3}y^{4}}{5})

Explanation Hindi:
(\left(\frac{125x^{-9}}{64y^{12}}\right)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}})। (-\frac{1}{3}) घात लेने पर व्युत्क्रम (\frac{4x^{3}y^{4}}{5}) मिलता है।

Explanation English:
We get (\left(\frac{125x^{-9}}{64y^{12}}\right)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}}). The power (-\frac{1}{3}) gives the reciprocal (\frac{4x^{3}y^{4}}{5}).

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}\right\)^{-1}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}\right\)^{-1})?

Explanation opens after your attempt

Correct Answer

A. \(9r^{6}s^{-8}\)

Step 1

Concept

Inside, \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\). Raising to (-1) gives \(9r^{6}s^{-8}\).

Step 2

Why this answer is correct

The correct answer is A. \(9r^{6}s^{-8}\). Inside, \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\). Raising to (-1) gives \(9r^{6}s^{-8}\).

Step 3

Exam Tip

अंदर \(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}\) है। (-1) घात लेने पर \(9r^{6}s^{-8}\) मिलता है।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
(\left(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}\right)^{-1}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}\right)^{-1})?

Options:
A. (9r^{6}s^{-8})
B. (\frac{1}{9}r^{-6}s^{8})
C. (9r^{-6}s^{8})
D. (\frac{1}{9}r^{6}s^{-8})

Correct Answer:
A. (9r^{6}s^{-8})

Explanation Hindi:
अंदर (\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}) है। (-1) घात लेने पर (9r^{6}s^{-8}) मिलता है।

Explanation English:
Inside, (\frac{9r^{-4}s^{3}}{81r^{2}s^{-5}}=\frac{1}{9}r^{-6}s^{8}). Raising to (-1) gives (9r^{6}s^{-8}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

\(\sqrt[3]{343a^{15}b^{12}}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt[3]{343a^{15}b^{12}}\)?

Explanation opens after your attempt

Correct Answer

A. \(7a^{5}b^{4}\)

Step 1

Concept

We have \(\sqrt[3]{343}=7\), \(\sqrt[3]{a^{15}}=a^{5}\), and \(\sqrt[3]{b^{12}}=b^{4}\). In exams, divide exponents by (3) under a cube root.

Step 2

Why this answer is correct

The correct answer is A. \(7a^{5}b^{4}\). We have \(\sqrt[3]{343}=7\), \(\sqrt[3]{a^{15}}=a^{5}\), and \(\sqrt[3]{b^{12}}=b^{4}\). In exams, divide exponents by (3) under a cube root.

Step 3

Exam Tip

\(\sqrt[3]{343}=7\), \(\sqrt[3]{a^{15}}=a^{5}\), और \(\sqrt[3]{b^{12}}=b^{4}\)। परीक्षा में घनमूल में घातों को (3) से भाग दें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
(\sqrt[3]{343a^{15}b^{12}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\sqrt[3]{343a^{15}b^{12}})?

Options:
A. (7a^{5}b^{4})
B. (7a^{4}b^{5})
C. (49a^{5}b^{4})
D. (7a^{3}b^{4})

Correct Answer:
A. (7a^{5}b^{4})

Explanation Hindi:
(\sqrt[3]{343}=7), (\sqrt[3]{a^{15}}=a^{5}), और (\sqrt[3]{b^{12}}=b^{4})। परीक्षा में घनमूल में घातों को (3) से भाग दें।

Explanation English:
We have (\sqrt[3]{343}=7), (\sqrt[3]{a^{15}}=a^{5}), and (\sqrt[3]{b^{12}}=b^{4}). In exams, divide exponents by (3) under a cube root.

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1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (\left\(x^{4}y^{-3}\right\)^{k}=x^{16}y^{-12}), तो (k) का मान क्या है?

If (\left\(x^{4}y^{-3}\right\)^{k}=x^{16}y^{-12}), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The left side has exponents (4k) and (-3k). Both (4k=16) and (-3k=-12) give (k=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The left side has exponents (4k) and (-3k). Both (4k=16) and (-3k=-12) give (k=4).

Step 3

Exam Tip

बाएँ पक्ष में घातें (4k) और (-3k) हैं। (4k=16) और (-3k=-12) दोनों से (k=4) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
यदि (\left(x^{4}y^{-3}\right)^{k}=x^{16}y^{-12}), तो (k) का मान क्या है?

Question English:
If (\left(x^{4}y^{-3}\right)^{k}=x^{16}y^{-12}), what is the value of (k)?

Options:
A. (2)
B. (3)
C. (4)
D. (5)

Correct Answer:
C. (4)

Explanation Hindi:
बाएँ पक्ष में घातें (4k) और (-3k) हैं। (4k=16) और (-3k=-12) दोनों से (k=4) मिलता है।

Explanation English:
The left side has exponents (4k) and (-3k). Both (4k=16) and (-3k=-12) give (k=4).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{p^{-5}q^{4}}{p^{-1}q^{-2}}\right\)^{-2}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{p^{-5}q^{4}}{p^{-1}q^{-2}}\right\)^{-2})?

Explanation opens after your attempt

Correct Answer

A. \(p^{8}q^{-12}\)

Step 1

Concept

Inside, (p^{-5-(-1)}q^{4-(-2)}=p^{-4}q^{6}). Raising to (-2) gives \(p^{8}q^{-12}\).

Step 2

Why this answer is correct

The correct answer is A. \(p^{8}q^{-12}\). Inside, (p^{-5-(-1)}q^{4-(-2)}=p^{-4}q^{6}). Raising to (-2) gives \(p^{8}q^{-12}\).

Step 3

Exam Tip

अंदर (p^{-5-(-1)}q^{4-(-2)}=p^{-4}q^{6}) है। (-2) घात देने पर \(p^{8}q^{-12}\) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 45

Question Hindi:
(\left(\frac{p^{-5}q^{4}}{p^{-1}q^{-2}}\right)^{-2}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{p^{-5}q^{4}}{p^{-1}q^{-2}}\right)^{-2})?

Options:
A. (p^{8}q^{-12})
B. (p^{-8}q^{12})
C. (p^{10}q^{-8})
D. (p^{-10}q^{8})

Correct Answer:
A. (p^{8}q^{-12})

Explanation Hindi:
अंदर (p^{-5-(-1)}q^{4-(-2)}=p^{-4}q^{6}) है। (-2) घात देने पर (p^{8}q^{-12}) मिलता है।

Explanation English:
Inside, (p^{-5-(-1)}q^{4-(-2)}=p^{-4}q^{6}). Raising to (-2) gives (p^{8}q^{-12}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (\left\(2x^{-1}y^{2}\right\)^{3}\cdot\left\(4x^{2}y^{-1}\right\)^{-1}) को \(cx^{r}y^{s}\) लिखा जाए, तो (c+r+s) का मान क्या है?

If (\left\(2x^{-1}y^{2}\right\)^{3}\cdot\left\(4x^{2}y^{-1}\right\)^{-1}) is written as \(cx^{r}y^{s}\), what is the value of (c+r+s)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{17}{4}\)

Step 1

Concept

The expression is \(8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=2x^{-5}y^{7}\). Hence (c+r+s=2-5+7=4).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{17}{4}\). The expression is \(8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=2x^{-5}y^{7}\). Hence (c+r+s=2-5+7=4).

Step 3

Exam Tip

अभिव्यक्ति \(8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=;2x^{-5}y^{7}\) है। इसलिए (c+r+s=2-5+7=4) है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
यदि (\left(2x^{-1}y^{2}\right)^{3}\cdot\left(4x^{2}y^{-1}\right)^{-1}) को (cx^{r}y^{s}) लिखा जाए, तो (c+r+s) का मान क्या है?

Question English:
If (\left(2x^{-1}y^{2}\right)^{3}\cdot\left(4x^{2}y^{-1}\right)^{-1}) is written as (cx^{r}y^{s}), what is the value of (c+r+s)?

Options:
A. (\frac{17}{4})
B. (\frac{15}{4})
C. (\frac{19}{4})
D. (\frac{21}{4})

Correct Answer:
A. (\frac{17}{4})

Explanation Hindi:
अभिव्यक्ति (8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=;2x^{-5}y^{7}) है। इसलिए (c+r+s=2-5+7=4) है।

Explanation English:
The expression is (8x^{-3}y^{6}\cdot\frac{1}{4}x^{-2}y=2x^{-5}y^{7}). Hence (c+r+s=2-5+7=4).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{-\frac{1}{3}}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{-\frac{1}{3}})?

Explanation opens after your attempt

Correct Answer

A. \(\frac{3x^{2}y^{3}}{4}\)

Step 1

Concept

We get (\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}}). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{3x^{2}y^{3}}{4}\).

Step 2

Why this answer is correct

The correct answer is A. \(\frac{3x^{2}y^{3}}{4}\). We get (\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}}). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{3x^{2}y^{3}}{4}\).

Step 3

Exam Tip

(\left\(\frac{64x^{-6}}{27y^{9}}\right\)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}})। \(-\frac{1}{3}\) घात लेने पर व्युत्क्रम \(\frac{3x^{2}y^{3}}{4}\) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
(\left(\frac{64x^{-6}}{27y^{9}}\right)^{-\frac{1}{3}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{64x^{-6}}{27y^{9}}\right)^{-\frac{1}{3}})?

Options:
A. (\frac{3x^{2}y^{3}}{4})
B. (\frac{4}{3x^{2}y^{3}})
C. (\frac{4x^{-2}}{3y^{3}})
D. (\frac{3y^{3}}{4x^{2}})

Correct Answer:
A. (\frac{3x^{2}y^{3}}{4})

Explanation Hindi:
(\left(\frac{64x^{-6}}{27y^{9}}\right)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}})। (-\frac{1}{3}) घात लेने पर व्युत्क्रम (\frac{3x^{2}y^{3}}{4}) मिलता है।

Explanation English:
We get (\left(\frac{64x^{-6}}{27y^{9}}\right)^{\frac{1}{3}}=\frac{4x^{-2}}{3y^{3}}). The power (-\frac{1}{3}) gives the reciprocal (\frac{3x^{2}y^{3}}{4}).

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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}\right\)^{-1}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}\right\)^{-1})?

Explanation opens after your attempt

Correct Answer

A. \(7r^{5}s^{-6}\)

Step 1

Concept

Inside, \(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}=\frac{1}{7}r^{-5}s^{6}\). Raising to (-1) gives \(7r^{5}s^{-6}\).

Step 2

Why this answer is correct

The correct answer is A. \(7r^{5}s^{-6}\). Inside, \(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}=\frac{1}{7}r^{-5}s^{6}\). Raising to (-1) gives \(7r^{5}s^{-6}\).

Step 3

Exam Tip

अंदर \(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}=\frac{1}{7}r^{-5}s^{6}\) है। (-1) घात लेने पर \(7r^{5}s^{-6}\) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
(\left(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}\right)^{-1}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}\right)^{-1})?

Options:
A. (7r^{5}s^{-6})
B. (\frac{1}{7}r^{-5}s^{6})
C. (7r^{-5}s^{6})
D. (\frac{1}{7}r^{5}s^{-6})

Correct Answer:
A. (7r^{5}s^{-6})

Explanation Hindi:
अंदर (\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}=\frac{1}{7}r^{-5}s^{6}) है। (-1) घात लेने पर (7r^{5}s^{-6}) मिलता है।

Explanation English:
Inside, (\frac{7r^{-3}s^{2}}{49r^{2}s^{-4}}=\frac{1}{7}r^{-5}s^{6}). Raising to (-1) gives (7r^{5}s^{-6}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

\(\sqrt[3]{216a^{12}b^{9}}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt[3]{216a^{12}b^{9}}\)?

Explanation opens after your attempt

Correct Answer

A. \(6a^{4}b^{3}\)

Step 1

Concept

We have \(\sqrt[3]{216}=6\), \(\sqrt[3]{a^{12}}=a^{4}\), and \(\sqrt[3]{b^{9}}=b^{3}\). In exams, divide exponents by (3) under a cube root.

Step 2

Why this answer is correct

The correct answer is A. \(6a^{4}b^{3}\). We have \(\sqrt[3]{216}=6\), \(\sqrt[3]{a^{12}}=a^{4}\), and \(\sqrt[3]{b^{9}}=b^{3}\). In exams, divide exponents by (3) under a cube root.

Step 3

Exam Tip

\(\sqrt[3]{216}=6\), \(\sqrt[3]{a^{12}}=a^{4}\), और \(\sqrt[3]{b^{9}}=b^{3}\)। परीक्षा में घनमूल में घातों को (3) से भाग दें।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
(\sqrt[3]{216a^{12}b^{9}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\sqrt[3]{216a^{12}b^{9}})?

Options:
A. (6a^{4}b^{3})
B. (6a^{3}b^{4})
C. (36a^{4}b^{3})
D. (6a^{6}b^{3})

Correct Answer:
A. (6a^{4}b^{3})

Explanation Hindi:
(\sqrt[3]{216}=6), (\sqrt[3]{a^{12}}=a^{4}), और (\sqrt[3]{b^{9}}=b^{3})। परीक्षा में घनमूल में घातों को (3) से भाग दें।

Explanation English:
We have (\sqrt[3]{216}=6), (\sqrt[3]{a^{12}}=a^{4}), and (\sqrt[3]{b^{9}}=b^{3}). In exams, divide exponents by (3) under a cube root.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि (\left\(x^{-3}y^{2}\right\)^{k}=x^{-12}y^{8}), तो (k) का मान क्या है?

If (\left\(x^{-3}y^{2}\right\)^{k}=x^{-12}y^{8}), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The left side has exponents (-3k) and (2k). Both (-3k=-12) and (2k=8) give (k=4).

Step 2

Why this answer is correct

The correct answer is C. (4). The left side has exponents (-3k) and (2k). Both (-3k=-12) and (2k=8) give (k=4).

Step 3

Exam Tip

बाएँ पक्ष में घातें (-3k) और (2k) हैं। (-3k=-12) और (2k=8) दोनों से (k=4) मिलता है।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
यदि (\left(x^{-3}y^{2}\right)^{k}=x^{-12}y^{8}), तो (k) का मान क्या है?

Question English:
If (\left(x^{-3}y^{2}\right)^{k}=x^{-12}y^{8}), what is the value of (k)?

Options:
A. (2)
B. (3)
C. (4)
D. (5)

Correct Answer:
C. (4)

Explanation Hindi:
बाएँ पक्ष में घातें (-3k) और (2k) हैं। (-3k=-12) और (2k=8) दोनों से (k=4) मिलता है।

Explanation English:
The left side has exponents (-3k) and (2k). Both (-3k=-12) and (2k=8) give (k=4).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\left\(\frac{m^{-4}n^{3}}{m^{2}n^{-5}}\right\)^{-1}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{m^{-4}n^{3}}{m^{2}n^{-5}}\right\)^{-1})?

Explanation opens after your attempt

Correct Answer

B. \(m^{6}n^{-8}\)

Step 1

Concept

Inside, \(m^{-4-2}n^{3-(-5)}=m^{-6}n^{8}\). Raising to (-1) gives \(m^{6}n^{-8}\).

Step 2

Why this answer is correct

The correct answer is B. \(m^{6}n^{-8}\). Inside, \(m^{-4-2}n^{3-(-5)}=m^{-6}n^{8}\). Raising to (-1) gives \(m^{6}n^{-8}\).

Step 3

Exam Tip

अंदर \(m^{-4-2}n^{3-(-5)}=m^{-6}n^{8}\) है। (-1) घात लेने पर \(m^{6}n^{-8}\) मिलता है।

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Question Page:
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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 44

Question Hindi:
(\left(\frac{m^{-4}n^{3}}{m^{2}n^{-5}}\right)^{-1}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{m^{-4}n^{3}}{m^{2}n^{-5}}\right)^{-1})?

Options:
A. (m^{-6}n^{8})
B. (m^{6}n^{-8})
C. (m^{-2}n^{-2})
D. (m^{2}n^{2})

Correct Answer:
B. (m^{6}n^{-8})

Explanation Hindi:
अंदर (m^{-4-2}n^{3-(-5)}=m^{-6}n^{8}) है। (-1) घात लेने पर (m^{6}n^{-8}) मिलता है।

Explanation English:
Inside, (m^{-4-2}n^{3-(-5)}=m^{-6}n^{8}). Raising to (-1) gives (m^{6}n^{-8}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{27x^{-3}}{8y^{6}}\right\)^{-\frac{1}{3}}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{27x^{-3}}{8y^{6}}\right\)^{-\frac{1}{3}})?

Explanation opens after your attempt

Correct Answer

A. \(\frac{2xy^{2}}{3}\)

Step 1

Concept

We get (\left\(\frac{27x^{-3}}{8y^{6}}\right\)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}), so the power \(-\frac{1}{3}\) gives its reciprocal \(\frac{2xy^{2}}{3}\). In exams, treat the negative fractional power as a reciprocal after rooting.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{2xy^{2}}{3}\). We get (\left\(\frac{27x^{-3}}{8y^{6}}\right\)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}), so the power \(-\frac{1}{3}\) gives its reciprocal \(\frac{2xy^{2}}{3}\). In exams, treat the negative fractional power as a reciprocal after rooting.

Step 3

Exam Tip

(\left\(\frac{27x^{-3}}{8y^{6}}\right\)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}), इसलिए \(-\frac{1}{3}\) घात देने पर उसका व्युत्क्रम \(\frac{2xy^{2}}{3}\) है। परीक्षा में भिन्न घात के बाद ऋणात्मक संकेत को व्युत्क्रम मानें।

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
(\left(\frac{27x^{-3}}{8y^{6}}\right)^{-\frac{1}{3}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{27x^{-3}}{8y^{6}}\right)^{-\frac{1}{3}})?

Options:
A. \(\frac{2xy^{2}}{3}\)
B. \(\frac{3}{2xy^{2}}\)
C. \(\frac{3x}{2y^{2}}\)
D. \(\frac{2y^{2}}{3x}\)

Correct Answer:
A. \(\frac{2xy^{2}}{3}\)

Explanation Hindi:
(\left(\frac{27x^{-3}}{8y^{6}}\right)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}), इसलिए (-\frac{1}{3}) घात देने पर उसका व्युत्क्रम (\frac{2xy^{2}}{3}) है। परीक्षा में भिन्न घात के बाद ऋणात्मक संकेत को व्युत्क्रम मानें।

Explanation English:
We get (\left(\frac{27x^{-3}}{8y^{6}}\right)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}), so the power (-\frac{1}{3}) gives its reciprocal (\frac{2xy^{2}}{3}). In exams, treat the negative fractional power as a reciprocal after rooting.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right\)^{-1}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right\)^{-1})?

Explanation opens after your attempt

Correct Answer

A. \(5m^{6}n^{-4}\)

Step 1

Concept

Inside, \(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}\), so raising to (-1) gives \(5m^{6}n^{-4}\). In exams, do not forget to invert the coefficient too.

Step 2

Why this answer is correct

The correct answer is A. \(5m^{6}n^{-4}\). Inside, \(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}\), so raising to (-1) gives \(5m^{6}n^{-4}\). In exams, do not forget to invert the coefficient too.

Step 3

Exam Tip

अंदर \(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}\), इसलिए (-1) घात लेने पर \(5m^{6}n^{-4}\) है। परीक्षा में गुणांक भी उलटना न भूलें।

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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
(\left(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right)^{-1}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}\right)^{-1})?

Options:
A. (5m^{6}n^{-4})
B. (\frac{1}{5}m^{-6}n^{4})
C. (5m^{-6}n^{4})
D. (\frac{1}{5}m^{6}n^{-4})

Correct Answer:
A. (5m^{6}n^{-4})

Explanation Hindi:
अंदर (\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}), इसलिए (-1) घात लेने पर (5m^{6}n^{-4}) है। परीक्षा में गुणांक भी उलटना न भूलें।

Explanation English:
Inside, (\frac{5m^{-2}n^{3}}{25m^{4}n^{-1}}=\frac{1}{5}m^{-6}n^{4}), so raising to (-1) gives (5m^{6}n^{-4}). In exams, do not forget to invert the coefficient too.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

\(\sqrt[3]{125a^{9}b^{6}}\) का सरल रूप क्या है?

What is the simplified form of \(\sqrt[3]{125a^{9}b^{6}}\)?

Explanation opens after your attempt

Correct Answer

A. \(5a^{3}b^{2}\)

Step 1

Concept

We have \(\sqrt[3]{125}=5\), \(\sqrt[3]{a^{9}}=a^{3}\), and \(\sqrt[3]{b^{6}}=b^{2}\). In exams, divide exponents by (3) under a cube root.

Step 2

Why this answer is correct

The correct answer is A. \(5a^{3}b^{2}\). We have \(\sqrt[3]{125}=5\), \(\sqrt[3]{a^{9}}=a^{3}\), and \(\sqrt[3]{b^{6}}=b^{2}\). In exams, divide exponents by (3) under a cube root.

Step 3

Exam Tip

\(\sqrt[3]{125}=5\), \(\sqrt[3]{a^{9}}=a^{3}\), और \(\sqrt[3]{b^{6}}=b^{2}\)। परीक्षा में घनमूल में घातों को (3) से भाग दें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-sqrt-3-125a-9-b-6

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
(\sqrt[3]{125a^{9}b^{6}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\sqrt[3]{125a^{9}b^{6}})?

Options:
A. (5a^{3}b^{2})
B. (25a^{3}b^{2})
C. (5a^{2}b^{3})
D. (5a^{6}b^{3})

Correct Answer:
A. (5a^{3}b^{2})

Explanation Hindi:
(\sqrt[3]{125}=5), (\sqrt[3]{a^{9}}=a^{3}), और (\sqrt[3]{b^{6}}=b^{2})। परीक्षा में घनमूल में घातों को (3) से भाग दें।

Explanation English:
We have (\sqrt[3]{125}=5), (\sqrt[3]{a^{9}}=a^{3}), and (\sqrt[3]{b^{6}}=b^{2}). In exams, divide exponents by (3) under a cube root.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि (\left\(x^{2}y^{-1}\right\)^{k}=x^{10}y^{-5}), तो (k) का मान क्या है?

If (\left\(x^{2}y^{-1}\right\)^{k}=x^{10}y^{-5}), what is the value of (k)?

Explanation opens after your attempt

Correct Answer

C. (5)

Step 1

Concept

The left side has exponents (2k) and (-k). Both (2k=10) and (-k=-5) give (k=5).

Step 2

Why this answer is correct

The correct answer is C. (5). The left side has exponents (2k) and (-k). Both (2k=10) and (-k=-5) give (k=5).

Step 3

Exam Tip

बाएँ पक्ष में घातें (2k) और (-k) हैं। (2k=10) और (-k=-5) दोनों से (k=5) मिलता है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/if-left-x-2-y-1-right-k-x-10-y-5-what-is-the-value-of-k

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
यदि (\left(x^{2}y^{-1}\right)^{k}=x^{10}y^{-5}), तो (k) का मान क्या है?

Question English:
If (\left(x^{2}y^{-1}\right)^{k}=x^{10}y^{-5}), what is the value of (k)?

Options:
A. (3)
B. (4)
C. (5)
D. (6)

Correct Answer:
C. (5)

Explanation Hindi:
बाएँ पक्ष में घातें (2k) और (-k) हैं। (2k=10) और (-k=-5) दोनों से (k=5) मिलता है।

Explanation English:
The left side has exponents (2k) and (-k). Both (2k=10) and (-k=-5) give (k=5).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}\right\)^{2}\cdot\frac{y^{12}}{x^{4}}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}\right\)^{2}\cdot\frac{y^{12}}{x^{4}})?

Explanation opens after your attempt

Correct Answer

A. \(4x^{4}\)

Step 1

Concept

Inside, \(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}=2x^{4}y^{-6}\), and its square is \(4x^{8}y^{-12}\). Multiplying by \(\frac{y^{12}}{x^{4}}\) gives \(4x^{4}\).

Step 2

Why this answer is correct

The correct answer is A. \(4x^{4}\). Inside, \(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}=2x^{4}y^{-6}\), and its square is \(4x^{8}y^{-12}\). Multiplying by \(\frac{y^{12}}{x^{4}}\) gives \(4x^{4}\).

Step 3

Exam Tip

अंदर \(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}=2x^{4}y^{-6}\), इसका वर्ग \(4x^{8}y^{-12}\) है। फिर \(\frac{y^{12}}{x^{4}}\) से गुणा करने पर \(4x^{4}\) मिलता है।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-left-frac-4x-3-y-2-2x-1-y-4-right-2-cdot-frac-y-12-x-4

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
(\left(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}\right)^{2}\cdot\frac{y^{12}}{x^{4}}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}\right)^{2}\cdot\frac{y^{12}}{x^{4}})?

Options:
A. (4x^{4})
B. (4y^{4})
C. (2x^{4})
D. (8x^{2})

Correct Answer:
A. (4x^{4})

Explanation Hindi:
अंदर (\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}=2x^{4}y^{-6}), इसका वर्ग (4x^{8}y^{-12}) है। फिर (\frac{y^{12}}{x^{4}}) से गुणा करने पर (4x^{4}) मिलता है।

Explanation English:
Inside, (\frac{4x^{3}y^{-2}}{2x^{-1}y^{4}}=2x^{4}y^{-6}), and its square is (4x^{8}y^{-12}). Multiplying by (\frac{y^{12}}{x^{4}}) gives (4x^{4}).

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
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- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

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Question Expert Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\left\(\frac{a^{-3}b^{2}}{a^{2}b^{-4}}\right\)^{-2}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{a^{-3}b^{2}}{a^{2}b^{-4}}\right\)^{-2})?

Explanation opens after your attempt

Correct Answer

A. \(a^{10}b^{-12}\)

Step 1

Concept

Inside, \(a^{-3-2}b^{2-(-4)}=a^{-5}b^{6}\), so raising to (-2) gives \(a^{10}b^{-12}\). In exams, a negative outer power changes the signs of both exponents.

Step 2

Why this answer is correct

The correct answer is A. \(a^{10}b^{-12}\). Inside, \(a^{-3-2}b^{2-(-4)}=a^{-5}b^{6}\), so raising to (-2) gives \(a^{10}b^{-12}\). In exams, a negative outer power changes the signs of both exponents.

Step 3

Exam Tip

अंदर \(a^{-3-2}b^{2-(-4)}=a^{-5}b^{6}\) है, इसलिए (-2) घात देने पर \(a^{10}b^{-12}\) मिलता है। परीक्षा में ऋणात्मक घात पर दोनों घातों के चिह्न बदलते हैं।

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AI Video Prompt 16:9 + 9:16

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Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

Brand:
- Name: Muft Shiksha
- Website: https://muftshiksha.com
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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-left-frac-a-3-b-2-a-2-b-4-right-2

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Expert
Level: 43

Question Hindi:
(\left(\frac{a^{-3}b^{2}}{a^{2}b^{-4}}\right)^{-2}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{a^{-3}b^{2}}{a^{2}b^{-4}}\right)^{-2})?

Options:
A. (a^{10}b^{-12})
B. (a^{-10}b^{12})
C. (a^{6}b^{-8})
D. (a^{-6}b^{8})

Correct Answer:
A. (a^{10}b^{-12})

Explanation Hindi:
अंदर (a^{-3-2}b^{2-(-4)}=a^{-5}b^{6}) है, इसलिए (-2) घात देने पर (a^{10}b^{-12}) मिलता है। परीक्षा में ऋणात्मक घात पर दोनों घातों के चिह्न बदलते हैं।

Explanation English:
Inside, (a^{-3-2}b^{2-(-4)}=a^{-5}b^{6}), so raising to (-2) gives (a^{10}b^{-12}). In exams, a negative outer power changes the signs of both exponents.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
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- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{3x^{-2}}{y^{-1}}\right\)^{3}\cdot\frac{y^{2}}{27}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{3x^{-2}}{y^{-1}}\right\)^{3}\cdot\frac{y^{2}}{27})?

Explanation opens after your attempt

Correct Answer

A. \(x^{-6}y^{5}\)

Step 1

Concept

\(\frac{3x^{-2}}{y^{-1}}=3x^{-2}y\), its cube is \(27x^{-6}y^{3}\), and multiplying by \(\frac{y^{2}}{27}\) gives \(x^{-6}y^{5}\). In exams, turn division by a negative power into multiplication.

Step 2

Why this answer is correct

The correct answer is A. \(x^{-6}y^{5}\). \(\frac{3x^{-2}}{y^{-1}}=3x^{-2}y\), its cube is \(27x^{-6}y^{3}\), and multiplying by \(\frac{y^{2}}{27}\) gives \(x^{-6}y^{5}\). In exams, turn division by a negative power into multiplication.

Step 3

Exam Tip

\(\frac{3x^{-2}}{y^{-1}}=3x^{-2}y\), इसका घन \(27x^{-6}y^{3}\) है, फिर \(\frac{y^{2}}{27}\) से गुणा करने पर \(x^{-6}y^{5}\) मिलता है। परीक्षा में भाग को ऋणात्मक घात से गुणा में बदलें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-left-frac-3x-2-y-1-right-3-cdot-frac-y-2-27

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 45

Question Hindi:
(\left(\frac{3x^{-2}}{y^{-1}}\right)^{3}\cdot\frac{y^{2}}{27}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{3x^{-2}}{y^{-1}}\right)^{3}\cdot\frac{y^{2}}{27})?

Options:
A. (x^{-6}y^{5})
B. (x^{6}y^{-5})
C. (x^{-6}y^{-1})
D. (x^{-2}y^{3})

Correct Answer:
A. (x^{-6}y^{5})

Explanation Hindi:
(\frac{3x^{-2}}{y^{-1}}=3x^{-2}y), इसका घन (27x^{-6}y^{3}) है, फिर (\frac{y^{2}}{27}) से गुणा करने पर (x^{-6}y^{5}) मिलता है। परीक्षा में भाग को ऋणात्मक घात से गुणा में बदलें।

Explanation English:
(\frac{3x^{-2}}{y^{-1}}=3x^{-2}y), its cube is (27x^{-6}y^{3}), and multiplying by (\frac{y^{2}}{27}) gives (x^{-6}y^{5}). In exams, turn division by a negative power into multiplication.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

यदि (\left\(x^{2}y^{3}\right\)^{n}=x^{8}y^{12}), तो (n) का मान क्या है?

If (\left\(x^{2}y^{3}\right\)^{n}=x^{8}y^{12}), what is the value of (n)?

Explanation opens after your attempt

Correct Answer

C. (4)

Step 1

Concept

The left side has exponents (2n) and (3n), so (2n=8) and (3n=12), giving (n=4). In exams, match exponents of both variables.

Step 2

Why this answer is correct

The correct answer is C. (4). The left side has exponents (2n) and (3n), so (2n=8) and (3n=12), giving (n=4). In exams, match exponents of both variables.

Step 3

Exam Tip

बाएँ पक्ष में घातें (2n) और (3n) हैं, इसलिए (2n=8) और (3n=12) से (n=4)। परीक्षा में दोनों चर की घात मिलाकर जांचें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/if-left-x-2-y-3-right-n-x-8-y-12-what-is-the-value-of-n

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 45

Question Hindi:
यदि (\left(x^{2}y^{3}\right)^{n}=x^{8}y^{12}), तो (n) का मान क्या है?

Question English:
If (\left(x^{2}y^{3}\right)^{n}=x^{8}y^{12}), what is the value of (n)?

Options:
A. (2)
B. (3)
C. (4)
D. (6)

Correct Answer:
C. (4)

Explanation Hindi:
बाएँ पक्ष में घातें (2n) और (3n) हैं, इसलिए (2n=8) और (3n=12) से (n=4)। परीक्षा में दोनों चर की घात मिलाकर जांचें।

Explanation English:
The left side has exponents (2n) and (3n), so (2n=8) and (3n=12), giving (n=4). In exams, match exponents of both variables.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{a^{3}b^{-2}}{a^{-1}b^{2}}\right\)^{2}) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{a^{3}b^{-2}}{a^{-1}b^{2}}\right\)^{2})?

Explanation opens after your attempt

Correct Answer

A. \(a^{8}b^{-8}\)

Step 1

Concept

Inside, \(a^{3-(-1)}b^{-2-2}=a^{4}b^{-4}\), and squaring gives \(a^{8}b^{-8}\). In exams, watch the sign when subtracting negative exponents.

Step 2

Why this answer is correct

The correct answer is A. \(a^{8}b^{-8}\). Inside, \(a^{3-(-1)}b^{-2-2}=a^{4}b^{-4}\), and squaring gives \(a^{8}b^{-8}\). In exams, watch the sign when subtracting negative exponents.

Step 3

Exam Tip

अंदर \(a^{3-(-1)}b^{-2-2}=a^{4}b^{-4}\), इसलिए वर्ग करने पर \(a^{8}b^{-8}\) है। परीक्षा में ऋणात्मक घात घटाते समय चिह्न पर ध्यान दें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-left-frac-a-3-b-2-a-1-b-2-right-2

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 45

Question Hindi:
(\left(\frac{a^{3}b^{-2}}{a^{-1}b^{2}}\right)^{2}) का सरल रूप क्या है?

Question English:
What is the simplified form of (\left(\frac{a^{3}b^{-2}}{a^{-1}b^{2}}\right)^{2})?

Options:
A. (a^{8}b^{-8})
B. (a^{4}b^{-4})
C. (a^{6}b^{-4})
D. (a^{2}b^{0})

Correct Answer:
A. (a^{8}b^{-8})

Explanation Hindi:
अंदर (a^{3-(-1)}b^{-2-2}=a^{4}b^{-4}), इसलिए वर्ग करने पर (a^{8}b^{-8}) है। परीक्षा में ऋणात्मक घात घटाते समय चिह्न पर ध्यान दें।

Explanation English:
Inside, (a^{3-(-1)}b^{-2-2}=a^{4}b^{-4}), and squaring gives (a^{8}b^{-8}). In exams, watch the sign when subtracting negative exponents.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

किस विकल्प में (\left\(ab^{-2}\right\)^{3}\cdot a^{-1}b^{5}) का सही सरल रूप है?

Which option gives the correct simplified form of (\left\(ab^{-2}\right\)^{3}\cdot a^{-1}b^{5})?

Explanation opens after your attempt

Correct Answer

A. \(a^{2}b^{-1}\)

Step 1

Concept

We have (\left\(ab^{-2}\right\)^{3}=a^{3}b^{-6}), and multiplying by \(a^{-1}b^{5}\) gives \(a^{2}b^{-1}\). In exams, add exponents separately for each variable.

Step 2

Why this answer is correct

The correct answer is A. \(a^{2}b^{-1}\). We have (\left\(ab^{-2}\right\)^{3}=a^{3}b^{-6}), and multiplying by \(a^{-1}b^{5}\) gives \(a^{2}b^{-1}\). In exams, add exponents separately for each variable.

Step 3

Exam Tip

(\left\(ab^{-2}\right\)^{3}=a^{3}b^{-6}), फिर \(a^{-1}b^{5}\) से गुणा करने पर \(a^{2}b^{-1}\) मिलता है। परीक्षा में हर चर की घात अलग-अलग जोड़ें।

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AI Video Prompt 16:9 + 9:16

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Question Page:
https://muftshiksha.com/question/which-option-gives-the-correct-simplified-form-of-left-ab-2-right-3-cdot-a-1-b-5

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 45

Question Hindi:
किस विकल्प में (\left(ab^{-2}\right)^{3}\cdot a^{-1}b^{5}) का सही सरल रूप है?

Question English:
Which option gives the correct simplified form of (\left(ab^{-2}\right)^{3}\cdot a^{-1}b^{5})?

Options:
A. (a^{2}b^{-1})
B. (a^{4}b^{-1})
C. (a^{2}b)
D. (a^{-2}b^{-1})

Correct Answer:
A. (a^{2}b^{-1})

Explanation Hindi:
(\left(ab^{-2}\right)^{3}=a^{3}b^{-6}), फिर (a^{-1}b^{5}) से गुणा करने पर (a^{2}b^{-1}) मिलता है। परीक्षा में हर चर की घात अलग-अलग जोड़ें।

Explanation English:
We have (\left(ab^{-2}\right)^{3}=a^{3}b^{-6}), and multiplying by (a^{-1}b^{5}) gives (a^{2}b^{-1}). In exams, add exponents separately for each variable.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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- Make 9:16 version for Shorts/Reels.
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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 45

(\left\(\frac{4x^{2}y^{-3}}{2x^{-1}y}\right\)^{-2}) का सरल रूप क्या है, जहाँ \(x\neq0\) और \(y\neq0\)?

What is the simplified form of (\left\(\frac{4x^{2}y^{-3}}{2x^{-1}y}\right\)^{-2}), where \(x\neq0\) and \(y\neq0\)?

Explanation opens after your attempt

Correct Answer

A. \(\frac{y^{8}}{4x^{6}}\)

Step 1

Concept

Inside, \(\frac{4x^{2}y^{-3}}{2x^{-1}y}=2x^{3}y^{-4}\), and raising to (-2) gives \(\frac{y^{8}}{4x^{6}}\). In exams, simplify inside the bracket first.

Step 2

Why this answer is correct

The correct answer is A. \(\frac{y^{8}}{4x^{6}}\). Inside, \(\frac{4x^{2}y^{-3}}{2x^{-1}y}=2x^{3}y^{-4}\), and raising to (-2) gives \(\frac{y^{8}}{4x^{6}}\). In exams, simplify inside the bracket first.

Step 3

Exam Tip

अंदर \(\frac{4x^{2}y^{-3}}{2x^{-1}y}=2x^{3}y^{-4}\), इसलिए घात (-2) देने पर \(\frac{y^{8}}{4x^{6}}\) मिलता है। परीक्षा में पहले कोष्ठक के अंदर सरल करें।

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AI Video Prompt 16:9 + 9:16

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Create a premium AI MCQ quiz video for Muft Shiksha in BOTH formats: 16:9 landscape and 9:16 vertical short.

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- Name: Muft Shiksha
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Question Page:
https://muftshiksha.com/question/what-is-the-simplified-form-of-left-frac-4x-2-y-3-2x-1-y-right-2-where-x-neq0-and-y-neq0

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 45

Question Hindi:
(\left(\frac{4x^{2}y^{-3}}{2x^{-1}y}\right)^{-2}) का सरल रूप क्या है, जहाँ (x\neq0) और (y\neq0)?

Question English:
What is the simplified form of (\left(\frac{4x^{2}y^{-3}}{2x^{-1}y}\right)^{-2}), where (x\neq0) and (y\neq0)?

Options:
A. (\frac{y^{8}}{4x^{6}})
B. (4x^{6}y^{-8})
C. (\frac{x^{6}}{4y^{8}})
D. (2x^{3}y^{-4})

Correct Answer:
A. (\frac{y^{8}}{4x^{6}})

Explanation Hindi:
अंदर (\frac{4x^{2}y^{-3}}{2x^{-1}y}=2x^{3}y^{-4}), इसलिए घात (-2) देने पर (\frac{y^{8}}{4x^{6}}) मिलता है। परीक्षा में पहले कोष्ठक के अंदर सरल करें।

Explanation English:
Inside, (\frac{4x^{2}y^{-3}}{2x^{-1}y}=2x^{3}y^{-4}), and raising to (-2) gives (\frac{y^{8}}{4x^{6}}). In exams, simplify inside the bracket first.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
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- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
- Final narration script.
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- Text overlays for 16:9 and 9:16.
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Open Question

Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

यदि \(x \neq 0\), तो (\dfrac{(2x)³\(3x^{-2}\)}{12x^{-1}}) का सरल रूप क्या है?

If \(x \neq 0\), what is the simplified form of (\dfrac{(2x)³\(3x^{-2}\)}{12x^{-1}})?

Explanation opens after your attempt

Correct Answer

A. \(,2x^2,\)

Step 1

Concept

The numerator is ((2x)³\(3x^{-2}\)=8x^-3\cdot 3x^{-2}=24x), and \(\dfrac{24x}{12x^{-1}}=2x^2\). In exams, simplify both coefficient and variable parts.

Step 2

Why this answer is correct

The correct answer is A. \(,2x^2,\). The numerator is ((2x)³\(3x^{-2}\)=8x^-3\cdot 3x^{-2}=24x), and \(\dfrac{24x}{12x^{-1}}=2x^2\). In exams, simplify both coefficient and variable parts.

Step 3

Exam Tip

ऊपर ((2x)³\(3x^{-2}\)=8x^-3\cdot 3x^{-2}=24x), और \(\dfrac{24x}{12x^{-1}}=2x^2\)। परीक्षा में coefficient और variable दोनों सरल करें।

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AI Video Prompt 16:9 + 9:16

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https://muftshiksha.com/question/if-x-neq-0-what-is-the-simplified-form-of-dfrac-2x-3-3x-2-12x-1

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
यदि (x \neq 0), तो (\dfrac{(2x)^3(3x^{-2})}{12x^{-1}}) का सरल रूप क्या है?

Question English:
If (x \neq 0), what is the simplified form of (\dfrac{(2x)^3(3x^{-2})}{12x^{-1}})?

Options:
A. (,2x^2,)
B. (,2x,)
C. (,\dfrac{2}{x^2},)
D. (,6x^2,)

Correct Answer:
A. (,2x^2,)

Explanation Hindi:
ऊपर ((2x)^3(3x^{-2})=8x^3\cdot 3x^{-2}=24x), और (\dfrac{24x}{12x^{-1}}=2x^2)। परीक्षा में coefficient और variable दोनों सरल करें।

Explanation English:
The numerator is ((2x)^3(3x^{-2})=8x^3\cdot 3x^{-2}=24x), and (\dfrac{24x}{12x^{-1}}=2x^2). In exams, simplify both coefficient and variable parts.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 44

(\(-4a^2b^{-3}\)\(3a^{-1}b^5\)) का गुणनफल क्या है?

What is the product of (\(-4a^2b^{-3}\)\(3a^{-1}b^5\))?

Explanation opens after your attempt

Correct Answer

A. \(,-12ab^2,\)

Step 1

Concept

The product of coefficients (-4) and (3) is (-12), and \(a^{2-1}b^{-3+5}=ab^2\). In exams, handle coefficients and exponents separately.

Step 2

Why this answer is correct

The correct answer is A. \(,-12ab^2,\). The product of coefficients (-4) and (3) is (-12), and \(a^{2-1}b^{-3+5}=ab^2\). In exams, handle coefficients and exponents separately.

Step 3

Exam Tip

गुणांक (-4) और (3) का गुणनफल (-12) है, और \(a^{2-1}b^{-3+5}=ab^2\) है। परीक्षा में गुणांक और घातांक अलग-अलग संभालें।

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Question Page:
https://muftshiksha.com/question/what-is-the-product-of-4a-2b-3-3a-1-b-5

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 44

Question Hindi:
((-4a^2b^{-3})(3a^{-1}b^5)) का गुणनफल क्या है?

Question English:
What is the product of ((-4a^2b^{-3})(3a^{-1}b^5))?

Options:
A. (,-12ab^2,)
B. (,-12a^3b^2,)
C. (,12ab^{-8},)
D. (,-a b^2,)

Correct Answer:
A. (,-12ab^2,)

Explanation Hindi:
गुणांक (-4) और (3) का गुणनफल (-12) है, और (a^{2-1}b^{-3+5}=ab^2) है। परीक्षा में गुणांक और घातांक अलग-अलग संभालें।

Explanation English:
The product of coefficients (-4) and (3) is (-12), and (a^{2-1}b^{-3+5}=ab^2). In exams, handle coefficients and exponents separately.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

यदि \(a \neq 0\) और \(b \neq 0\), तो \(\dfrac{6a^3b^2}{2ab^{-1}}\) का सरल रूप क्या है?

If \(a \neq 0\) and \(b \neq 0\), what is the simplified form of \(\dfrac{6a^3b^2}{2ab^{-1}}\)?

Explanation opens after your attempt

Correct Answer

A. \(,3a^2b^3,\)

Step 1

Concept

The coefficient is \(\dfrac{6}{2}=3\), \(a^{3-1}=a^2\), and \(b^{2-(-1)}=b^3\). In exams, the sign changes when subtracting a negative exponent.

Step 2

Why this answer is correct

The correct answer is A. \(,3a^2b^3,\). The coefficient is \(\dfrac{6}{2}=3\), \(a^{3-1}=a^2\), and \(b^{2-(-1)}=b^3\). In exams, the sign changes when subtracting a negative exponent.

Step 3

Exam Tip

गुणांक \(\dfrac{6}{2}=3\), \(a^{3-1}=a^2\) और \(b^{2-(-1)}=b^3\) है। परीक्षा में हर के ऋणात्मक घातांक को घटाते समय sign बदलता है।

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Question Page:
https://muftshiksha.com/question/if-a-neq-0-and-b-neq-0-what-is-the-simplified-form-of-dfrac-6a-3b-2-2ab-1

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 43

Question Hindi:
यदि (a \neq 0) और (b \neq 0), तो (\dfrac{6a^3b^2}{2ab^{-1}}) का सरल रूप क्या है?

Question English:
If (a \neq 0) and (b \neq 0), what is the simplified form of (\dfrac{6a^3b^2}{2ab^{-1}})?

Options:
A. (,3a^2b^3,)
B. (,3a^2b,)
C. (,3a^4b,)
D. (,\dfrac{3a^2}{b^3},)

Correct Answer:
A. (,3a^2b^3,)

Explanation Hindi:
गुणांक (\dfrac{6}{2}=3), (a^{3-1}=a^2) और (b^{2-(-1)}=b^3) है। परीक्षा में हर के ऋणात्मक घातांक को घटाते समय sign बदलता है।

Explanation English:
The coefficient is (\dfrac{6}{2}=3), (a^{3-1}=a^2), and (b^{2-(-1)}=b^3). In exams, the sign changes when subtracting a negative exponent.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question Hard Mathematics Polynomials Operations on real numbers and the laws of exponents Class 10 Level 43

(\(2x^2y\)\(-3xy^2\)) का गुणनफल क्या है?

What is the product of (\(2x^2y\)\(-3xy^2\))?

Explanation opens after your attempt

Correct Answer

A. \(,-6x^3y^3,\)

Step 1

Concept

The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.

Step 2

Why this answer is correct

The correct answer is A. \(,-6x^3y^3,\). The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.

Step 3

Exam Tip

गुणांक (2) और (-3) का गुणनफल (-6) है, और समान चरों की घातें जुड़ती हैं। परीक्षा में sign और exponents दोनों ध्यान से देखें।

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AI Video Prompt 16:9 + 9:16

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- Name: Muft Shiksha
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- Do not add wrong facts. Do not change the question, options or answer.

Question Page:
https://muftshiksha.com/question/what-is-the-product-of-2x-2y-3xy-2

MCQ Data:
Class: Class 10
Subject: Mathematics
Chapter: Polynomials
Topic: Operations on real numbers and the laws of exponents
Difficulty: Hard
Level: 43

Question Hindi:
((2x^2y)(-3xy^2)) का गुणनफल क्या है?

Question English:
What is the product of ((2x^2y)(-3xy^2))?

Options:
A. (,-6x^3y^3,)
B. (,-6x^2y^2,)
C. (,6x^3y^3,)
D. (,-x^3y^3,)

Correct Answer:
A. (,-6x^3y^3,)

Explanation Hindi:
गुणांक (2) और (-3) का गुणनफल (-6) है, और समान चरों की घातें जुड़ती हैं। परीक्षा में sign और exponents दोनों ध्यान से देखें।

Explanation English:
The product of coefficients (2) and (-3) is (-6), and powers of like variables are added. In exams, watch both the sign and the exponents carefully.

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

Custom Support:
- Make 16:9 version for YouTube/Facebook.
- Make 9:16 version for Shorts/Reels.
- Add Hindi-English natural voice-over.
- Add readable subtitles.
- Add light background music, low volume.
- Keep all text inside safe margins.
- Use smooth transitions, no clutter, no watermark except Muft Shiksha branding.
- Formula/Math/Chemistry text must stay exactly readable; use LaTeX-style clean rendering where needed.

Output Needed:
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