Concept-wise Practice

exponents MCQ Questions for Class 10

exponents se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

Practice Questions

181 questions tagged with exponents.

यदि \(\dfrac{2^5 \times 8}{4^2}\) को घात के रूप में सरल किया जाए, तो इसका मान क्या होगा?

If \(\dfrac{2^5 \times 8}{4^2}\) is simplified using exponents, what is its value?

Explanation opens after your attempt
Correct Answer

A. (,16,)

Step 1

Concept

Here \(8=2^3\) and (42=\(2^2\)2=24), so \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\). In exams, converting numbers to the same base is useful.

Step 2

Why this answer is correct

The correct answer is A. (,16,). Here \(8=2^3\) and (42=\(2^2\)2=24), so \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\). In exams, converting numbers to the same base is useful.

Step 3

Exam Tip

यहां \(8=2^3\) और (42=\(2^2\)2=24), इसलिए \(\dfrac{2^5 \times 2^3}{2^4}=2^4=16\)। परीक्षा में सभी संख्याओं को समान आधार में बदलना उपयोगी होता है।

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सरलीकृत कीजिए: (\(3^2\)3 \div 34) का मान किसके बराबर है?

Simplify: (\(3^2\)3 \div 34) is equal to which value?

Explanation opens after your attempt
Correct Answer

A. \(,3^2,\)

Step 1

Concept

By exponent laws, (\(3^2\)3=36) and \(3^6 \div 3^4=3^2\). In exams, apply power of a power first and then the division law.

Step 2

Why this answer is correct

The correct answer is A. \(,3^2,\). By exponent laws, (\(3^2\)3=36) and \(3^6 \div 3^4=3^2\). In exams, apply power of a power first and then the division law.

Step 3

Exam Tip

घात के नियम से (\(3^2\)3=36) और \(3^6 \div 3^4=3^2\) होता है। परीक्षा में पहले power of power का नियम लगाएं फिर division का।

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यदि \(2^{x-1}=32\) है तो (x) का मान क्या है?

If \(2^{x-1}=32\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (6)

Step 1

Concept

\(32=2^5\), so (x-1=5). This gives (x=6).

Step 2

Why this answer is correct

The correct answer is C. (6). \(32=2^5\), so (x-1=5). This gives (x=6).

Step 3

Exam Tip

\(32=2^5\), इसलिए (x-1=5) है। इससे (x=6) मिलता है।

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यदि (x=-4) है तो \(x^4+x^3\) का मान क्या है?

If (x=-4), what is the value of \(x^4+x^3\)?

Explanation opens after your attempt
Correct Answer

B. (192)

Step 1

Concept

((-4)4=256) and ((-4)3=-64). Hence (256-64=192).

Step 2

Why this answer is correct

The correct answer is B. (192). ((-4)4=256) and ((-4)3=-64). Hence (256-64=192).

Step 3

Exam Tip

((-4)4=256) और ((-4)3=-64) है। इसलिए (256-64=192) है।

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(\(6x^2y\)\(3xy^4\)) का गुणनफल क्या है?

What is the product of (\(6x^2y\)\(3xy^4\))?

Explanation opens after your attempt
Correct Answer

A. \(18x^3y^5\)

Step 1

Concept

The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.

Step 2

Why this answer is correct

The correct answer is A. \(18x^3y^5\). The coefficient is (18), \(x^{2+1}=x^3\), and \(y^{1+4}=y^5\). Add exponents of like bases.

Step 3

Exam Tip

गुणांक (18), \(x^{2+1}=x^3\) और \(y^{1+4}=y^5\) है। समान आधार की घातें जोड़ें।

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यदि (q(x)=x-3+2x-2-4x) है तो (q(-2)) का मान क्या है?

If (q(x)=x-3+2x-2-4x), what is the value of (q(-2))?

Explanation opens after your attempt
Correct Answer

C. (8)

Step 1

Concept

(q(-2)=(-2)3+2(-2)2-4(-2)=-8+8+8=8). Use parentheses for negative substitution.

Step 2

Why this answer is correct

The correct answer is C. (8). (q(-2)=(-2)3+2(-2)2-4(-2)=-8+8+8=8). Use parentheses for negative substitution.

Step 3

Exam Tip

(q(-2)=(-2)3+2(-2)2-4(-2)=-8+8+8=8)। ऋणात्मक मान रखते समय कोष्ठक लगाएँ।

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(\(2a^2b^3\)2) का सही विस्तार क्या है?

What is the correct expansion of (\(2a^2b^3\)2)?

Explanation opens after your attempt
Correct Answer

A. \(4a^4b^6\)

Step 1

Concept

The outside exponent applies to the coefficient and all powers. Thus (\(2a^2b^3\)2=4a-4b-6).

Step 2

Why this answer is correct

The correct answer is A. \(4a^4b^6\). The outside exponent applies to the coefficient and all powers. Thus (\(2a^2b^3\)2=4a-4b-6).

Step 3

Exam Tip

बाहरी घात गुणांक और सभी घातों पर लगती है। इसलिए (\(2a^2b^3\)2=4a-4b-6) है।

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\(\frac{4^3\cdot2^{-1}}{8}\) का मान क्या है?

What is the value of \(\frac{4^3\cdot2^{-1}}{8}\)?

Explanation opens after your attempt
Correct Answer

B. (4)

Step 1

Concept

(43=\(2^2\)3=26), \(2^{-1}\), and \(8=2^3\). The total exponent is (6-1-3=2), so the value is \(2^2=4\).

Step 2

Why this answer is correct

The correct answer is B. (4). (43=\(2^2\)3=26), \(2^{-1}\), and \(8=2^3\). The total exponent is (6-1-3=2), so the value is \(2^2=4\).

Step 3

Exam Tip

(43=\(2^2\)3=26), \(2^{-1}\) और \(8=2^3\) है। कुल घात (6-1-3=2) है इसलिए मान \(2^2=4\) है।

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यदि \(5^{x-2}=125\) है तो (x) का मान क्या है?

If \(5^{x-2}=125\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

C. (5)

Step 1

Concept

\(125=5^3\), so (x-2=3). This gives (x=5).

Step 2

Why this answer is correct

The correct answer is C. (5). \(125=5^3\), so (x-2=3). This gives (x=5).

Step 3

Exam Tip

\(125=5^3\), इसलिए (x-2=3) है। इससे (x=5) मिलता है।

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यदि (x=-3) है तो \(x^4+x^3\) का मान क्या है?

If (x=-3), what is the value of \(x^4+x^3\)?

Explanation opens after your attempt
Correct Answer

B. (54)

Step 1

Concept

((-3)4=81) and ((-3)3=-27). Hence (81-27=54).

Step 2

Why this answer is correct

The correct answer is B. (54). ((-3)4=81) and ((-3)3=-27). Hence (81-27=54).

Step 3

Exam Tip

((-3)4=81) और ((-3)3=-27) है। इसलिए (81-27=54) है।

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(\(5x^3y\)\(2xy^2\)) का गुणनफल क्या है?

What is the product of (\(5x^3y\)\(2xy^2\))?

Explanation opens after your attempt
Correct Answer

A. \(10x^4y^3\)

Step 1

Concept

The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.

Step 2

Why this answer is correct

The correct answer is A. \(10x^4y^3\). The coefficient is (10), \(x^{3+1}=x^4\), and \(y^{1+2}=y^3\). Add exponents of like bases.

Step 3

Exam Tip

गुणांक (10), \(x^{3+1}=x^4\) और \(y^{1+2}=y^3\) है। समान आधार की घातें जोड़ें।

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(\frac{\(3x^2\)2}{9x}) का सरल रूप क्या है यदि \(x\neq0\)?

What is the simplified form of (\frac{\(3x^2\)2}{9x}) if \(x\neq0\)?

Explanation opens after your attempt
Correct Answer

B. \(x^3\)

Step 1

Concept

(\(3x^2\)2=9x-4). Then \(\frac{9x^4}{9x}=x^3\).

Step 2

Why this answer is correct

The correct answer is B. \(x^3\). (\(3x^2\)2=9x-4). Then \(\frac{9x^4}{9x}=x^3\).

Step 3

Exam Tip

(\(3x^2\)2=9x-4) होता है। फिर \(\frac{9x^4}{9x}=x^3\) है।

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यदि (a=3) है तो \(a^2+a^{-1}\) का मान क्या है?

If (a=3), what is the value of \(a^2+a^{-1}\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{28}{3}\)

Step 1

Concept

\(3^2=9\) and \(3^{-1}=\frac{1}{3}\). Thus the sum is \(9+\frac{1}{3}=\frac{28}{3}\).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{28}{3}\). \(3^2=9\) and \(3^{-1}=\frac{1}{3}\). Thus the sum is \(9+\frac{1}{3}=\frac{28}{3}\).

Step 3

Exam Tip

\(3^2=9\) और \(3^{-1}=\frac{1}{3}\) है। इसलिए योग \(9+\frac{1}{3}=\frac{28}{3}\) है।

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\(\frac{27^2}{3^4}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{27^2}{3^4}\)?

Explanation opens after your attempt
Correct Answer

A. \(3^2\)

Step 1

Concept

(272=\(3^3\)2=36). Therefore \(\frac{3^6}{3^4}=3^2\).

Step 2

Why this answer is correct

The correct answer is A. \(3^2\). (272=\(3^3\)2=36). Therefore \(\frac{3^6}{3^4}=3^2\).

Step 3

Exam Tip

(272=\(3^3\)2=36) होता है। इसलिए \(\frac{3^6}{3^4}=3^2\) है।

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\(\frac{3^4\cdot2^4}{6^3}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{3^4\cdot2^4}{6^3}\)?

Explanation opens after your attempt
Correct Answer

A. (6)

Step 1

Concept

(34\cdot24=\(3\cdot2\)4=64). Therefore \(\frac{6^4}{6^3}=6\).

Step 2

Why this answer is correct

The correct answer is A. (6). (34\cdot24=\(3\cdot2\)4=64). Therefore \(\frac{6^4}{6^3}=6\).

Step 3

Exam Tip

(34\cdot24=\(3\cdot2\)4=64) है। इसलिए \(\frac{6^4}{6^3}=6\) है।

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\(\frac{7^3}{7^{-1}\cdot7^2}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{7^3}{7^{-1}\cdot7^2}\)?

Explanation opens after your attempt
Correct Answer

A. \(7^2\)

Step 1

Concept

The denominator exponent is (-1+2=1). Therefore the total exponent is (3-1=2).

Step 2

Why this answer is correct

The correct answer is A. \(7^2\). The denominator exponent is (-1+2=1). Therefore the total exponent is (3-1=2).

Step 3

Exam Tip

हर में घात (-1+2=1) है। इसलिए कुल घात (3-1=2) होती है।

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\(5^4\cdot5^{-2}\cdot5^3\) का सरल रूप क्या है?

What is the simplified form of \(5^4\cdot5^{-2}\cdot5^3\)?

Explanation opens after your attempt
Correct Answer

A. \(5^5\)

Step 1

Concept

For the same base, exponents add as (4-2+3=5). Hence the simplified form is \(5^5\).

Step 2

Why this answer is correct

The correct answer is A. \(5^5\). For the same base, exponents add as (4-2+3=5). Hence the simplified form is \(5^5\).

Step 3

Exam Tip

समान आधार में घातें (4-2+3=5) जुड़ती हैं। इसलिए सरल रूप \(5^5\) है।

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यदि \(3^{x+1}=81\) है तो (x) का मान क्या है?

If \(3^{x+1}=81\), what is the value of (x)?

Explanation opens after your attempt
Correct Answer

B. (3)

Step 1

Concept

\(81=3^4\), so (x+1=4). This gives (x=3).

Step 2

Why this answer is correct

The correct answer is B. (3). \(81=3^4\), so (x+1=4). This gives (x=3).

Step 3

Exam Tip

\(81=3^4\), इसलिए (x+1=4) है। इससे (x=3) मिलता है।

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यदि (x=-2) है तो \(x^4-2x^3\) का मान क्या है?

If (x=-2), what is the value of \(x^4-2x^3\)?

Explanation opens after your attempt
Correct Answer

C. (32)

Step 1

Concept

((-2)4=16) and ((-2)3=-8). Hence (16-2(-8)=32).

Step 2

Why this answer is correct

The correct answer is C. (32). ((-2)4=16) and ((-2)3=-8). Hence (16-2(-8)=32).

Step 3

Exam Tip

((-2)4=16) और ((-2)3=-8) है। इसलिए (16-2(-8)=32) है।

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(\(3x^2y\)\(4xy^3\)) का गुणनफल क्या है?

What is the product of (\(3x^2y\)\(4xy^3\))?

Explanation opens after your attempt
Correct Answer

A. \(12x^3y^4\)

Step 1

Concept

The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.

Step 2

Why this answer is correct

The correct answer is A. \(12x^3y^4\). The coefficient is (12), \(x^{2+1}=x^3\), and \(y^{1+3}=y^4\). Add exponents of like bases.

Step 3

Exam Tip

गुणांक (12), \(x^{2+1}=x^3\) और \(y^{1+3}=y^4\) है। समान आधार की घातें जोड़ें।

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(\frac{\(2x^3\)2}{4x-2}) का सरल रूप क्या है यदि \(x\neq0\)?

What is the simplified form of (\frac{\(2x^3\)2}{4x-2}) if \(x\neq0\)?

Explanation opens after your attempt
Correct Answer

B. \(x^4\)

Step 1

Concept

(\(2x^3\)2=4x-6). Then \(\frac{4x^6}{4x^2}=x^4\).

Step 2

Why this answer is correct

The correct answer is B. \(x^4\). (\(2x^3\)2=4x-6). Then \(\frac{4x^6}{4x^2}=x^4\).

Step 3

Exam Tip

(\(2x^3\)2=4x-6) होता है। फिर \(\frac{4x^6}{4x^2}=x^4\) है।

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यदि (a=2) है तो \(a^3+a^{-1}\) का मान क्या है?

If (a=2), what is the value of \(a^3+a^{-1}\)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{17}{2}\)

Step 1

Concept

\(2^3=8\) and \(2^{-1}=\frac{1}{2}\). Thus the sum is \(8+\frac{1}{2}=\frac{17}{2}\).

Step 2

Why this answer is correct

The correct answer is B. \(\frac{17}{2}\). \(2^3=8\) and \(2^{-1}=\frac{1}{2}\). Thus the sum is \(8+\frac{1}{2}=\frac{17}{2}\).

Step 3

Exam Tip

\(2^3=8\) और \(2^{-1}=\frac{1}{2}\) है। इसलिए योग \(8+\frac{1}{2}=\frac{17}{2}\) है।

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\(\frac{16^2}{2^5}\) का मान क्या है?

What is the value of \(\frac{16^2}{2^5}\)?

Explanation opens after your attempt
Correct Answer

A. \(2^3\)

Step 1

Concept

(162=\(2^4\)2=28). Therefore \(\frac{2^8}{2^5}=2^3\).

Step 2

Why this answer is correct

The correct answer is A. \(2^3\). (162=\(2^4\)2=28). Therefore \(\frac{2^8}{2^5}=2^3\).

Step 3

Exam Tip

(162=\(2^4\)2=28) होता है। इसलिए \(\frac{2^8}{2^5}=2^3\) है।

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(\left\(\frac{2^3\cdot5^3}{10^2}\right\)) का सरल रूप क्या है?

What is the simplified form of (\left\(\frac{2^3\cdot5^3}{10^2}\right\))?

Explanation opens after your attempt
Correct Answer

A. (10)

Step 1

Concept

Since (23\cdot53=(10)3), \(\frac{10^3}{10^2}=10\). Combine equal powers first.

Step 2

Why this answer is correct

The correct answer is A. (10). Since (23\cdot53=(10)3), \(\frac{10^3}{10^2}=10\). Combine equal powers first.

Step 3

Exam Tip

क्योंकि (23\cdot53=(10)3), इसलिए \(\frac{10^3}{10^2}=10\)। समान घात वाले गुणकों को पहले जोड़ें।

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\(\frac{3^2\cdot3^{-4}}{3^{-3}}\) का सरल रूप क्या है?

What is the simplified form of \(\frac{3^2\cdot3^{-4}}{3^{-3}}\)?

Explanation opens after your attempt
Correct Answer

B. \(3^1\)

Step 1

Concept

Combine the exponents as (2-4-(-3)=1). The sign changes when subtracting a negative exponent.

Step 2

Why this answer is correct

The correct answer is B. \(3^1\). Combine the exponents as (2-4-(-3)=1). The sign changes when subtracting a negative exponent.

Step 3

Exam Tip

घातों को (2-4-(-3)=1) करें। ऋणात्मक घात घटाते समय चिह्न बदलता है।

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\(2^3\cdot2^{-5}\cdot2^4\) का सरल रूप क्या है?

What is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?

Explanation opens after your attempt
Correct Answer

A. \(2^2\)

Step 1

Concept

For the same base, exponents add as (3-5+4=2). Hence the simplified form is \(2^2\).

Step 2

Why this answer is correct

The correct answer is A. \(2^2\). For the same base, exponents add as (3-5+4=2). Hence the simplified form is \(2^2\).

Step 3

Exam Tip

समान आधार में घातें (3-5+4=2) जुड़ती हैं। इसलिए सरल रूप \(2^2\) है।

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\(7^2\cdot7^0\cdot7^4\) का सरल रूप क्या है?

What is the simplified form of \(7^2\cdot7^0\cdot7^4\)?

Explanation opens after your attempt
Correct Answer

A. \(7^6\)

Step 1

Concept

For the same base, the exponents add as (2+0+4=6). Hence the simplified form is \(7^6\).

Step 2

Why this answer is correct

The correct answer is A. \(7^6\). For the same base, the exponents add as (2+0+4=6). Hence the simplified form is \(7^6\).

Step 3

Exam Tip

समान आधार में घातें (2+0+4=6) जुड़ती हैं। इसलिए सरल रूप \(7^6\) है।

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\(42a^7\div6a^4\) का सरल रूप क्या है यदि \(a\neq0\)?

What is the simplified form of \(42a^7\div6a^4\) if \(a\neq0\)?

Explanation opens after your attempt
Correct Answer

A. \(7a^3\)

Step 1

Concept

\(\frac{42}{6}=7\) and \(\frac{a^7}{a^4}=a^3\). Therefore the answer is \(7a^3\).

Step 2

Why this answer is correct

The correct answer is A. \(7a^3\). \(\frac{42}{6}=7\) and \(\frac{a^7}{a^4}=a^3\). Therefore the answer is \(7a^3\).

Step 3

Exam Tip

\(\frac{42}{6}=7\) और \(\frac{a^7}{a^4}=a^3\) है। इसलिए उत्तर \(7a^3\) है।

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\(5x^4\cdot2x^3\) का गुणनफल क्या है?

What is the product of \(5x^4\cdot2x^3\)?

Explanation opens after your attempt
Correct Answer

B. \(10x^7\)

Step 1

Concept

The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).

Step 2

Why this answer is correct

The correct answer is B. \(10x^7\). The coefficients give \(5\cdot2=10\), and \(x^4\cdot x^3=x^7\). So the product is \(10x^7\).

Step 3

Exam Tip

गुणांक \(5\cdot2=10\) और \(x^4\cdot x^3=x^7\) है। इसलिए गुणनफल \(10x^7\) है।

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\(6x^2+8x^2\) का सरल रूप क्या है?

What is the simplified form of \(6x^2+8x^2\)?

Explanation opens after your attempt
Correct Answer

A. \(14x^2\)

Step 1

Concept

These are like terms, so the coefficients (6+8=14) are added. The exponent (2) does not change.

Step 2

Why this answer is correct

The correct answer is A. \(14x^2\). These are like terms, so the coefficients (6+8=14) are added. The exponent (2) does not change.

Step 3

Exam Tip

ये समान पद हैं इसलिए गुणांक (6+8=14) जुड़ते हैं। घात (2) नहीं बदलती।

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