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?
#polynomials
#real-numbers
#exponents
#same-base
A (,16,)
B (,8,)
C (,32,)
D (,64,)
Explanation opens after your attempt
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?
#polynomials
#real-numbers
#exponents
#laws-of-exponents
A \(,3^2,\)
B \(,3^4,\)
C \(,3^6,\)
D \(,3^8,\)
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)?
#polynomials
#exponents
#equations
A (4)
B (5)
C (6)
D (7)
Explanation opens after your attempt
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 \(x^4+x^3\)?
#polynomials
#negative substitution
#exponents
A (128)
B (192)
C (256)
D (320)
Explanation opens after your attempt
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 (\(6x^2y\)\(3xy^4\))?
#polynomials
#monomial multiplication
#exponents
A \(18x^3y^5\)
B \(9x^3y^5\)
C \(18x^2y^4\)
D \(18x^4y^4\)
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))?
#polynomials
#negative substitution
#exponents
A (0)
B (4)
C (8)
D (12)
Explanation opens after your attempt
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 )?
#polynomials
#monomial powers
#exponents
A \(4a^4b^6\)
B \(2a^4b^6\)
C \(4a^2b^3\)
D \(4a^4b^5\)
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-4 b-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-4 b-6 ).
Step 3
Exam Tip
बाहरी घात गुणांक और सभी घातों पर लगती है। इसलिए (\(2a^2b^3\)2 =4a-4 b-6 ) है।
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\(\frac{4^3\cdot2^{-1}}{8}\) का मान क्या है?
What is the value of \(\frac{4^3\cdot2^{-1}}{8}\)?
#polynomials
#powers of two
#exponents
A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
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)?
#polynomials
#exponents
#equations
A (3)
B (4)
C (5)
D (6)
Explanation opens after your attempt
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 \(x^4+x^3\)?
#polynomials
#negative substitution
#exponents
A (27)
B (54)
C (81)
D (108)
Explanation opens after your attempt
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 (\(5x^3y\)\(2xy^2\))?
#polynomials
#monomial multiplication
#exponents
A \(10x^4y^3\)
B \(7x^4y^3\)
C \(10x^3y^2\)
D \(10x^6y^2\)
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 \(x\neq0\)?
#polynomials
#monomial division
#exponents
A \(x^2\)
B \(x^3\)
C \(3x^3\)
D \(9x^3\)
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 \(a^2+a^{-1}\)?
#polynomials
#substitution
#exponents
A \(\frac{26}{3}\)
B \(\frac{28}{3}\)
C (10)
D \(\frac{10}{3}\)
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 \(\frac{27^2}{3^4}\)?
#polynomials
#powers of three
#exponents
A \(3^2\)
B \(3^4\)
C \(3^6\)
D \(3^8\)
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 \(\frac{3^4\cdot2^4}{6^3}\)?
#polynomials
#real numbers
#exponents
A (6)
B \(6^2\)
C (12)
D (36)
Explanation opens after your attempt
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 \(\frac{7^3}{7^{-1}\cdot7^2}\)?
#polynomials
#exponents
#quotient law
A \(7^2\)
B \(7^6\)
C \(7^{-4}\)
D \(7^0\)
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 \(5^4\cdot5^{-2}\cdot5^3\)?
#polynomials
#exponents
#negative powers
A \(5^5\)
B \(5^9\)
C \(5^{-1}\)
D \(5^{24}\)
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)?
#polynomials
#exponents
#equations
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
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 \(x^4-2x^3\)?
#polynomials
#negative substitution
#exponents
A (0)
B (16)
C (32)
D (48)
Explanation opens after your attempt
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 (\(3x^2y\)\(4xy^3\))?
#polynomials
#monomial multiplication
#exponents
A \(12x^3y^4\)
B \(7x^3y^4\)
C \(12x^2y^3\)
D \(12x^4y^3\)
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 \(x\neq0\)?
#polynomials
#monomial division
#exponents
A \(x^2\)
B \(x^4\)
C \(2x^4\)
D \(4x^4\)
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 \(a^3+a^{-1}\)?
#polynomials
#substitution
#exponents
A \(\frac{15}{2}\)
B \(\frac{17}{2}\)
C (9)
D (7)
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 \(\frac{16^2}{2^5}\)?
#polynomials
#powers of two
#exponents
A \(2^3\)
B \(2^4\)
C \(2^5\)
D \(2^8\)
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\(\frac{2^3\cdot5^3}{10^2}\right\))?
#polynomials
#real numbers
#exponents
A (10)
B (20)
C (40)
D (100)
Explanation opens after your attempt
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 \(\frac{3^2\cdot3^{-4}}{3^{-3}}\)?
#polynomials
#exponents
#quotient law
A \(3^{-5}\)
B \(3^1\)
C \(3^{-9}\)
D \(3^9\)
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 \(2^3\cdot2^{-5}\cdot2^4\)?
#polynomials
#exponents
#negative powers
A \(2^2\)
B \(2^{-6}\)
C \(2^{12}\)
D \(2^{-2}\)
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 \(7^2\cdot7^0\cdot7^4\)?
#polynomials
#mixed exponent law
#exponents
A \(7^6\)
B \(7^8\)
C \(7^0\)
D \(7^1\)
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 \(a\neq0\)?
#polynomials
#monomial division
#exponents
A \(7a^3\)
B \(36a^3\)
C \(7a^{11}\)
D \(252a^3\)
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 \(5x^4\cdot2x^3\)?
#polynomials
#monomial multiplication
#exponents
A \(7x^7\)
B \(10x^7\)
C \(10x^{12}\)
D (10x)
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 \(6x^2+8x^2\)?
#polynomials
#like terms
#exponents
A \(14x^2\)
B \(14x^4\)
C \(48x^2\)
D \(2x^2\)
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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