\(2^3\cdot2^{-5}\cdot2^4\) का सरल रूप क्या है?
What is the simplified form of \(2^3\cdot2^{-5}\cdot2^4\)?
#polynomials
#exponents
#negative powers
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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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\(\frac{3^2\cdot3^{-4}}{3^{-3}}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{3^2\cdot3^{-4}}{3^{-3}}\)?
#polynomials
#exponents
#quotient law
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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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यदि \(x\neq0\) है तो (\frac{\(x^3\)2 \cdot x^{-4}}{x}) का सरल रूप क्या है?
If \(x\neq0\), what is the simplified form of (\frac{\(x^3\)2 \cdot x^{-4}}{x})?
#polynomials
#algebraic exponents
#simplification
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A (x)
B \(x^2\)
C \(x^{-1}\)
D \(x^3\)
Explanation opens after your attempt
Step 1
Concept
First (\(x^3\)2 =x-6 ), then the exponent is (6-4-1=1). So the answer is (x).
Step 2
Why this answer is correct
The correct answer is A. (x). First (\(x^3\)2 =x-6 ), then the exponent is (6-4-1=1). So the answer is (x).
Step 3
Exam Tip
पहले (\(x^3\)2 =x-6 ), फिर घात (6-4-1=1) है। इसलिए उत्तर (x) 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
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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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\(\frac{16^2}{2^5}\) का मान क्या है?
What is the value of \(\frac{16^2}{2^5}\)?
#polynomials
#powers of two
#exponents
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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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((0.2)^{-2}) का मान क्या है?
What is the value of ((0.2)^{-2})?
#polynomials
#negative exponent
#decimals
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A (5)
B (10)
C (25)
D (0.04)
Explanation opens after your attempt
Step 1
Concept
\(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.
Step 2
Why this answer is correct
The correct answer is C. (25). \(0.2=\frac{1}{5}\), so ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25). Converting decimals to fractions helps.
Step 3
Exam Tip
\(0.2=\frac{1}{5}\), इसलिए ((0.2)^{-2}=\left\(\frac{1}{5}\right\)^{-2}=25)। दशमलव को भिन्न में बदलना आसान होता है।
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(\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\)) का मान क्या है?
What is the value of (\left\(\frac{3}{2}\right\)^{-2}\cdot\left\(\frac{9}{4}\right\))?
#polynomials
#fraction powers
#negative exponent
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A (1)
B \(\frac{9}{4}\)
C \(\frac{4}{9}\)
D \(\frac{81}{16}\)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).
Step 2
Why this answer is correct
The correct answer is A. (1). (\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}). Hence \(\frac{4}{9}\cdot\frac{9}{4}=1\).
Step 3
Exam Tip
(\left\(\frac{3}{2}\right\)^{-2}=\left\(\frac{2}{3}\right\)2 =\frac{4}{9}) है। इसलिए \(\frac{4}{9}\cdot\frac{9}{4}=1\) 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
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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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(\(x^2y^3\)2 ) का सही सरल रूप क्या है?
What is the correct simplified form of (\(x^2y^3\)2 )?
#polynomials
#monomial powers
#exponent law
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A \(x^4y^6\)
B \(x^4y^5\)
C \(x^2y^6\)
D \(x^4+y^6\)
Explanation opens after your attempt
Correct Answer
A. \(x^4y^6\)
Step 1
Concept
The outside exponent multiplies the exponents of both factors. Hence (\(x^2y^3\)2 =x-4 y-6 ).
Step 2
Why this answer is correct
The correct answer is A. \(x^4y^6\). The outside exponent multiplies the exponents of both factors. Hence (\(x^2y^3\)2 =x-4 y-6 ).
Step 3
Exam Tip
बाहरी घात दोनों कारकों की घातों से गुणा होती है। इसलिए (\(x^2y^3\)2 =x-4 y-6 ) है।
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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
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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 (p(x)=2x-2 -3x+1) है तो (p(2)) का मान क्या है?
If (p(x)=2x-2 -3x+1), what is the value of (p(2))?
#polynomials
#polynomial value
#real numbers
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(p(2)=2(2)2 -3(2)+1=8-6+1=3). Evaluate powers first while substituting.
Step 2
Why this answer is correct
The correct answer is B. (3). (p(2)=2(2)2 -3(2)+1=8-6+1=3). Evaluate powers first while substituting.
Step 3
Exam Tip
(p(2)=2(2)2 -3(2)+1=8-6+1=3)। प्रतिस्थापन में पहले घात निकालें।
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यदि (q(x)=x-3 -2x-2 +x) है तो (q(-1)) का मान क्या है?
If (q(x)=x-3 -2x-2 +x), what is the value of (q(-1))?
#polynomials
#substitution
#negative numbers
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A (-4)
B (-2)
C (0)
D (4)
Explanation opens after your attempt
Step 1
Concept
(q(-1)=(-1)3 -2(-1)2 +(-1)=-1-2-1=-4). Use parentheses with negative substitution.
Step 2
Why this answer is correct
The correct answer is A. (-4). (q(-1)=(-1)3 -2(-1)2 +(-1)=-1-2-1=-4). Use parentheses with negative substitution.
Step 3
Exam Tip
(q(-1)=(-1)3 -2(-1)2 +(-1)=-1-2-1=-4)। ऋणात्मक संख्या पर कोष्ठक लगाना जरूरी है।
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\(3x^2+5x^2-2x^2\) का सरल रूप क्या है?
What is the simplified form of \(3x^2+5x^2-2x^2\)?
#polynomials
#like terms
#addition subtraction
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A \(6x^2\)
B \(6x^6\)
C \(10x^2\)
D (6x)
Explanation opens after your attempt
Correct Answer
A. \(6x^2\)
Step 1
Concept
The coefficients of like terms are (3+5-2=6). Thus the simplified form is \(6x^2\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^2\). The coefficients of like terms are (3+5-2=6). Thus the simplified form is \(6x^2\).
Step 3
Exam Tip
समान पदों के गुणांक (3+5-2=6) होते हैं। इसलिए सरल रूप \(6x^2\) है।
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((x+2)+(3x-5)) का सरल रूप क्या है?
What is the simplified form of ((x+2)+(3x-5))?
#polynomials
#addition
#like terms
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A (4x-3)
B (4x+7)
C (2x-3)
D (3x+3)
Explanation opens after your attempt
Step 1
Concept
Combining like terms gives (x+3x=4x) and (2-5=-3). So the answer is (4x-3).
Step 2
Why this answer is correct
The correct answer is A. (4x-3). Combining like terms gives (x+3x=4x) and (2-5=-3). So the answer is (4x-3).
Step 3
Exam Tip
समान पद जोड़ने पर (x+3x=4x) और (2-5=-3) है। इसलिए उत्तर (4x-3) है।
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((5x+1)-(2x-4)) का सरल रूप क्या है?
What is the simplified form of ((5x+1)-(2x-4))?
#polynomials
#subtraction
#brackets
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A (3x-3)
B (3x+5)
C (7x-3)
D (7x+5)
Explanation opens after your attempt
Step 1
Concept
The minus sign applies to both terms in the second bracket. (5x+1-2x+4=3x+5).
Step 2
Why this answer is correct
The correct answer is B. (3x+5). The minus sign applies to both terms in the second bracket. (5x+1-2x+4=3x+5).
Step 3
Exam Tip
ऋण चिह्न दूसरे कोष्ठक के दोनों पदों पर लगेगा। (5x+1-2x+4=3x+5) है।
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(2x\(3x^2-4x+1\)) का विस्तार क्या है?
What is the expansion of (2x\(3x^2-4x+1\))?
#polynomials
#distributive law
#expansion
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A \(6x^3-8x^2+2x\)
B \(6x^2-8x+2\)
C \(5x^3-6x^2+3x\)
D \(6x^3+8x^2+2x\)
Explanation opens after your attempt
Correct Answer
A. \(6x^3-8x^2+2x\)
Step 1
Concept
Multiply (2x) by every term. This gives \(6x^3-8x^2+2x\).
Step 2
Why this answer is correct
The correct answer is A. \(6x^3-8x^2+2x\). Multiply (2x) by every term. This gives \(6x^3-8x^2+2x\).
Step 3
Exam Tip
(2x) को हर पद से गुणा करें। इससे \(6x^3-8x^2+2x\) मिलता है।
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((x+3)(x+2)) का विस्तार क्या है?
What is the expansion of ((x+3)(x+2))?
#polynomials
#multiplication
#binomials
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A \(x^2+5x+6\)
B \(x^2+6x+5\)
C \(x^2+5\)
D (2x+5)
Explanation opens after your attempt
Correct Answer
A. \(x^2+5x+6\)
Step 1
Concept
By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.
Step 2
Why this answer is correct
The correct answer is A. \(x^2+5x+6\). By distribution, \(x^2+2x+3x+6=x^2+5x+6\). The middle term forms by combining like terms.
Step 3
Exam Tip
वितरण नियम से \(x^2+2x+3x+6=x^2+5x+6\)। मध्य पद समान पद जोड़कर बनता है।
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((x-4)(x+1)) का विस्तार क्या है?
What is the expansion of ((x-4)(x+1))?
#polynomials
#binomial multiplication
#signs
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A \(x^2-3x-4\)
B \(x^2+3x-4\)
C \(x^2-5x+4\)
D \(x^2-4\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-3x-4\)
Step 1
Concept
Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-3x-4\). Multiplying gives \(x^2+x-4x-4=x^2-3x-4\). Pay close attention to signs.
Step 3
Exam Tip
गुणा करने पर \(x^2+x-4x-4=x^2-3x-4\) मिलता है। चिह्नों पर विशेष ध्यान दें।
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((2x+3)(x-2)) का विस्तार क्या है?
What is the expansion of ((2x+3)(x-2))?
#polynomials
#binomial multiplication
#expansion
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A \(2x^2-x-6\)
B \(2x^2+x-6\)
C \(2x^2-4x+3\)
D \(2x^2-6\)
Explanation opens after your attempt
Correct Answer
A. \(2x^2-x-6\)
Step 1
Concept
By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.
Step 2
Why this answer is correct
The correct answer is A. \(2x^2-x-6\). By distribution, \(2x^2-4x+3x-6=2x^2-x-6\). Combine like terms at the end.
Step 3
Exam Tip
वितरण से \(2x^2-4x+3x-6=2x^2-x-6\) है। समान पदों को अंत में जोड़ें।
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((x+5)2 ) का सही विस्तार क्या है?
What is the correct expansion of ((x+5)2 )?
#polynomials
#identity
#square of sum
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A \(x^2+10x+25\)
B \(x^2+25\)
C \(x^2+5x+25\)
D \(x^2+10x+5\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+10x+25\)
Step 1
Concept
Use ((a+b)2 =a-2 +2ab+b-2 ). Here the middle term is \(2\cdot x\cdot5=10x\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x+25\). Use ((a+b)2 =a-2 +2ab+b-2 ). Here the middle term is \(2\cdot x\cdot5=10x\).
Step 3
Exam Tip
((a+b)2 =a-2 +2ab+b-2 ) लगाएँ। यहाँ मध्य पद \(2\cdot x\cdot5=10x\) है।
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((x-6)2 ) का सही विस्तार क्या है?
What is the correct expansion of ((x-6)2 )?
#polynomials
#identity
#square of difference
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A \(x^2-12x+36\)
B \(x^2+12x+36\)
C \(x^2-36\)
D \(x^2-6x+36\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-12x+36\)
Step 1
Concept
((a-b)2 =a-2 -2ab+b-2 ). Therefore the middle term is (-12x).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-12x+36\). ((a-b)2 =a-2 -2ab+b-2 ). Therefore the middle term is (-12x).
Step 3
Exam Tip
((a-b)2 =a-2 -2ab+b-2 ) होता है। इसलिए मध्य पद (-12x) है।
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((x+7)(x-7)) का सरल रूप क्या है?
What is the simplified form of ((x+7)(x-7))?
#polynomials
#identity
#difference of squares
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A \(x^2-49\)
B \(x^2+49\)
C \(x^2-14x+49\)
D \(x^2+14x-49\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-49\)
Step 1
Concept
This is of the form ((a+b)(a-b)=a-2 -b-2 ). Hence ((x+7)(x-7)=x-2 -49).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-49\). This is of the form ((a+b)(a-b)=a-2 -b-2 ). Hence ((x+7)(x-7)=x-2 -49).
Step 3
Exam Tip
यह ((a+b)(a-b)=a-2 -b-2 ) का रूप है। इसलिए ((x+7)(x-7)=x-2 -49) है।
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\(49x^2-64\) का गुणनखंड रूप क्या है?
What is the factorized form of \(49x^2-64\)?
#polynomials
#factorization
#difference of squares
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A ((7x-8)(7x+8))
B ((49x-8)(x+8))
C ((7x-8)2 )
D ((7x+8)2 )
Explanation opens after your attempt
Correct Answer
A. ((7x-8)(7x+8))
Step 1
Concept
(49x-2 -64=(7x)2 -82 ). Apply the difference of squares identity.
Step 2
Why this answer is correct
The correct answer is A. ((7x-8)(7x+8)). (49x-2 -64=(7x)2 -82 ). Apply the difference of squares identity.
Step 3
Exam Tip
(49x-2 -64=(7x)2 -82 ) है। अंतर के वर्ग का नियम लगाएँ।
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\(x^2+14x+49\) किसके बराबर है?
What is \(x^2+14x+49\) equal to?
#polynomials
#perfect square
#identity
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A ((x+7)2 )
B ((x-7)2 )
C ((x+14)2 )
D \(x^2+49\)
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 )
Step 1
Concept
This is \(x^2+2\cdot x\cdot7+7^2\). Therefore it is ((x+7)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 ). This is \(x^2+2\cdot x\cdot7+7^2\). Therefore it is ((x+7)2 ).
Step 3
Exam Tip
यह \(x^2+2\cdot x\cdot7+7^2\) है। इसलिए यह ((x+7)2 ) है।
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\(x^2-16x+64\) किसके बराबर है?
What is \(x^2-16x+64\) equal to?
#polynomials
#perfect square
#factorization
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A ((x-8)2 )
B ((x+8)2 )
C ((x-16)2 )
D \(x^2-64\)
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 )
Step 1
Concept
This is of the form \(x^2-2\cdot x\cdot8+8^2\). Hence ((x-8)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 ). This is of the form \(x^2-2\cdot x\cdot8+8^2\). Hence ((x-8)2 ) is correct.
Step 3
Exam Tip
यह \(x^2-2\cdot x\cdot8+8^2\) का रूप है। इसलिए ((x-8)2 ) सही है।
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यदि (m+n=9) और (mn=18) है तो \(m^2+n^2\) का मान क्या है?
If (m+n=9) and (mn=18), what is the value of \(m^2+n^2\)?
#polynomials
#identity
#real numbers
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A (45)
B (54)
C (63)
D (81)
Explanation opens after your attempt
Step 1
Concept
(m-2 +n-2 =(m+n)2 -2mn=81-36=45). Using identities makes calculation shorter.
Step 2
Why this answer is correct
The correct answer is A. (45). (m-2 +n-2 =(m+n)2 -2mn=81-36=45). Using identities makes calculation shorter.
Step 3
Exam Tip
(m-2 +n-2 =(m+n)2 -2mn=81-36=45)। पहचान का उपयोग गणना को छोटा करता है।
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यदि (a-b=5) और (ab=6) है तो \(a^2+b^2\) का मान क्या है?
If (a-b=5) and (ab=6), what is the value of \(a^2+b^2\)?
#polynomials
#identity
#applications
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A (25)
B (31)
C (37)
D (49)
Explanation opens after your attempt
Step 1
Concept
(a-2 +b-2 =(a-b)2 +2ab=25+12=37). Choosing the correct identity is important.
Step 2
Why this answer is correct
The correct answer is C. (37). (a-2 +b-2 =(a-b)2 +2ab=25+12=37). Choosing the correct identity is important.
Step 3
Exam Tip
(a-2 +b-2 =(a-b)2 +2ab=25+12=37)। सही पहचान चुनना जरूरी है।
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\(99^2\) को पहचान से निकालने पर सही मान क्या है?
Using an identity, what is the correct value of \(99^2\)?
#polynomials
#identity
#mental math
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A (9801)
B (9901)
C (10001)
D (9701)
Explanation opens after your attempt
Step 1
Concept
(992 =(100-1)2 =10000-200+1=9801). Using a nearby number identity gives quick calculation.
Step 2
Why this answer is correct
The correct answer is A. (9801). (992 =(100-1)2 =10000-200+1=9801). Using a nearby number identity gives quick calculation.
Step 3
Exam Tip
(992 =(100-1)2 =10000-200+1=9801)। निकट संख्या की पहचान तेज गणना देती है।
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\(102^2\) का मान क्या है?
What is the value of \(102^2\)?
#polynomials
#identity
#square
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A (10404)
B (10440)
C (10004)
D (10204)
Explanation opens after your attempt
Correct Answer
A. (10404)
Step 1
Concept
(1022 =(100+2)2 =10000+400+4=10404). Do not forget the middle term in ((a+b)2 ).
Step 2
Why this answer is correct
The correct answer is A. (10404). (1022 =(100+2)2 =10000+400+4=10404). Do not forget the middle term in ((a+b)2 ).
Step 3
Exam Tip
(1022 =(100+2)2 =10000+400+4=10404)। ((a+b)2 ) में मध्य पद न भूलें।
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\(53\cdot47\) का मान पहचान से क्या है?
Using an identity, what is the value of \(53\cdot47\)?
#polynomials
#identity
#product
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A (2491)
B (2509)
C (2391)
D (2809)
Explanation opens after your attempt
Step 1
Concept
(53\cdot47=(50+3)(50-3)=502 -32 =2491). This uses the difference of squares identity.
Step 2
Why this answer is correct
The correct answer is A. (2491). (53\cdot47=(50+3)(50-3)=502 -32 =2491). This uses the difference of squares identity.
Step 3
Exam Tip
(53\cdot47=(50+3)(50-3)=502 -32 =2491)। यह अंतर के वर्ग का उपयोग है।
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\(1.5^2-0.5^2\) का मान क्या है?
What is the value of \(1.5^2-0.5^2\)?
#polynomials
#real numbers
#difference of squares
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A (1)
B (2)
C (2.5)
D (3)
Explanation opens after your attempt
Step 1
Concept
Using (a-2 -b-2 =(a-b)(a+b)), ((1.5-0.5)(1.5+0.5)=1\cdot2=2). Identities also work with decimals.
Step 2
Why this answer is correct
The correct answer is B. (2). Using (a-2 -b-2 =(a-b)(a+b)), ((1.5-0.5)(1.5+0.5)=1\cdot2=2). Identities also work with decimals.
Step 3
Exam Tip
(a-2 -b-2 =(a-b)(a+b)) से ((1.5-0.5)(1.5+0.5)=1\cdot2=2)। पहचान दशमलव में भी लागू होती है।
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(\left\(\frac{1}{3}\right\)^{-2}+\left\(\frac{1}{2}\right\)^{-2}) का मान क्या है?
What is the value of (\left\(\frac{1}{3}\right\)^{-2}+\left\(\frac{1}{2}\right\)^{-2})?
#polynomials
#negative powers
#fractions
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A (5)
B (13)
C \(\frac{13}{36}\)
D (36)
Explanation opens after your attempt
Step 1
Concept
(\left\(\frac{1}{3}\right\)^{-2}=9) and (\left\(\frac{1}{2}\right\)^{-2}=4). The sum is (13).
Step 2
Why this answer is correct
The correct answer is B. (13). (\left\(\frac{1}{3}\right\)^{-2}=9) and (\left\(\frac{1}{2}\right\)^{-2}=4). The sum is (13).
Step 3
Exam Tip
(\left\(\frac{1}{3}\right\)^{-2}=9) और (\left\(\frac{1}{2}\right\)^{-2}=4) है। योग (13) है।
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यदि (a=3) और (b=2) है तो \(a^2b+ab^2\) का मान क्या है?
If (a=3) and (b=2), what is the value of \(a^2b+ab^2\)?
#polynomials
#factorization
#substitution
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A (24)
B (30)
C (36)
D (42)
Explanation opens after your attempt
Step 1
Concept
(a-2 b+ab-2 =ab(a+b)). Thus \(3\cdot2\cdot5=30\).
Step 2
Why this answer is correct
The correct answer is B. (30). (a-2 b+ab-2 =ab(a+b)). Thus \(3\cdot2\cdot5=30\).
Step 3
Exam Tip
(a-2 b+ab-2 =ab(a+b)) है। इसलिए \(3\cdot2\cdot5=30\) है।
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\(2x^3+6x^2\) का सामान्य गुणनखंड निकालने पर क्या मिलेगा?
What is obtained by taking the common factor from \(2x^3+6x^2\)?
#polynomials
#common factor
#factorization
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A (2x-2 (x+3))
B (2x\(x^2+3\))
C (x-2 (2x+6x))
D (6x-2 (x+1))
Explanation opens after your attempt
Correct Answer
A. (2x-2 (x+3))
Step 1
Concept
The common factor in both terms is \(2x^2\). Hence the form is (2x-2 (x+3)).
Step 2
Why this answer is correct
The correct answer is A. (2x-2 (x+3)). The common factor in both terms is \(2x^2\). Hence the form is (2x-2 (x+3)).
Step 3
Exam Tip
दोनों पदों में सामान्य गुणनखंड \(2x^2\) है। इसलिए रूप (2x-2 (x+3)) है।
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\(15a^4b^2\div5a^2b\) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?
What is the simplified form of \(15a^4b^2\div5a^2b\) if \(a\neq0\) and \(b\neq0\)?
#polynomials
#monomial division
#exponent laws
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A \(3a^2b\)
B \(10a^2b\)
C \(3a^6b^3\)
D \(75a^2b\)
Explanation opens after your attempt
Correct Answer
A. \(3a^2b\)
Step 1
Concept
The coefficient is \(\frac{15}{5}=3\), \(a^{4-2}=a^2\), and \(b^{2-1}=b\). So the answer is \(3a^2b\).
Step 2
Why this answer is correct
The correct answer is A. \(3a^2b\). The coefficient is \(\frac{15}{5}=3\), \(a^{4-2}=a^2\), and \(b^{2-1}=b\). So the answer is \(3a^2b\).
Step 3
Exam Tip
गुणांक \(\frac{15}{5}=3\), \(a^{4-2}=a^2\) और \(b^{2-1}=b\) है। इसलिए उत्तर \(3a^2b\) 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
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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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यदि (x=2) है तो \(3x^3-4x^2+5\) का मान क्या है?
If (x=2), what is the value of \(3x^3-4x^2+5\)?
#polynomials
#value of expression
#substitution
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A (11)
B (13)
C (15)
D (17)
Explanation opens after your attempt
Step 1
Concept
Substituting gives (3(8)-4(4)+5=24-16+5=13). Calculating powers first is the correct order.
Step 2
Why this answer is correct
The correct answer is B. (13). Substituting gives (3(8)-4(4)+5=24-16+5=13). Calculating powers first is the correct order.
Step 3
Exam Tip
मान रखने पर (3(8)-4(4)+5=24-16+5=13)। घात पहले निकालना सही क्रम 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
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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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\(\frac{x^5y^{-2}}{x^2y^{-4}}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of \(\frac{x^5y^{-2}}{x^2y^{-4}}\) if \(x\neq0\) and \(y\neq0\)?
#polynomials
#negative exponents
#division
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A \(x^3y^2\)
B \(x^7y^{-6}\)
C \(x^3y^{-6}\)
D \(x^7y^2\)
Explanation opens after your attempt
Correct Answer
A. \(x^3y^2\)
Step 1
Concept
The exponent of (x) is (5-2=3), and that of (y) is (-2-(-4)=2). Hence it is \(x^3y^2\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3y^2\). The exponent of (x) is (5-2=3), and that of (y) is (-2-(-4)=2). Hence it is \(x^3y^2\).
Step 3
Exam Tip
(x) की घात (5-2=3) और (y) की घात (-2-(-4)=2) है। इसलिए \(x^3y^2\) है।
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(\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of (\left\(\frac{x^{-2}}{y^{-3}}\right\)^{-1}) if \(x\neq0\) and \(y\neq0\)?
#polynomials
#negative exponent
#complex simplification
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A \(x^2y^{-3}\)
B \(x^{-2}y^3\)
C \(\frac{y^3}{x^2}\)
D \(\frac{x^2}{y^3}\)
Explanation opens after your attempt
Correct Answer
D. \(\frac{x^2}{y^3}\)
Step 1
Concept
Inside, \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\). The outside power (-1) gives \(\frac{x^2}{y^3}\).
Step 2
Why this answer is correct
The correct answer is D. \(\frac{x^2}{y^3}\). Inside, \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\). The outside power (-1) gives \(\frac{x^2}{y^3}\).
Step 3
Exam Tip
अंदर \(\frac{x^{-2}}{y^{-3}}=x^{-2}y^3\) है। बाहरी (-1) घात से \(\frac{x^2}{y^3}\) मिलता है।
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(\left\(2^3\right\)0 +5^{-1}) का मान क्या है?
What is the value of (\left\(2^3\right\)0 +5^{-1})?
#polynomials
#zero exponent
#negative exponent
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A \(\frac{1}{5}\)
B \(\frac{6}{5}\)
C (8)
D \(\frac{9}{5}\)
Explanation opens after your attempt
Correct Answer
B. \(\frac{6}{5}\)
Step 1
Concept
(\left\(2^3\right\)0 =1) and \(5^{-1}=\frac{1}{5}\). Therefore the sum is \(\frac{6}{5}\).
Step 2
Why this answer is correct
The correct answer is B. \(\frac{6}{5}\). (\left\(2^3\right\)0 =1) and \(5^{-1}=\frac{1}{5}\). Therefore the sum is \(\frac{6}{5}\).
Step 3
Exam Tip
(\left\(2^3\right\)0 =1) और \(5^{-1}=\frac{1}{5}\) है। इसलिए योग \(\frac{6}{5}\) है।
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\(4^{-1}+2^{-2}\) का मान क्या है?
What is the value of \(4^{-1}+2^{-2}\)?
#polynomials
#negative powers
#real numbers
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A \(\frac{1}{2}\)
B \(\frac{1}{4}\)
C \(\frac{3}{4}\)
D (6)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2}\)
Step 1
Concept
\(4^{-1}=\frac{1}{4}\) and \(2^{-2}=\frac{1}{4}\). So the sum is \(\frac{1}{2}\).
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2}\). \(4^{-1}=\frac{1}{4}\) and \(2^{-2}=\frac{1}{4}\). So the sum is \(\frac{1}{2}\).
Step 3
Exam Tip
\(4^{-1}=\frac{1}{4}\) और \(2^{-2}=\frac{1}{4}\) है। इसलिए योग \(\frac{1}{2}\) है।
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\(2^5\cdot4^{-1}\) का मान क्या है?
What is the value of \(2^5\cdot4^{-1}\)?
#polynomials
#powers of two
#negative exponent
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A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(4^{-1}=\(2^2\)^{-1}=2^{-2}). Hence \(2^5\cdot2^{-2}=2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). (4^{-1}=\(2^2\)^{-1}=2^{-2}). Hence \(2^5\cdot2^{-2}=2^3=8\).
Step 3
Exam Tip
(4^{-1}=\(2^2\)^{-1}=2^{-2}) है। इसलिए \(2^5\cdot2^{-2}=2^3=8\) है।
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((2x-3)2 ) का विस्तार क्या है?
What is the expansion of ((2x-3)2 )?
#polynomials
#identity
#binomial square
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A \(4x^2-12x+9\)
B \(4x^2-6x+9\)
C \(2x^2-12x+9\)
D \(4x^2-9\)
Explanation opens after your attempt
Correct Answer
A. \(4x^2-12x+9\)
Step 1
Concept
Use ((a-b)2 =a-2 -2ab+b-2 ). Here (a=2x) and (b=3).
Step 2
Why this answer is correct
The correct answer is A. \(4x^2-12x+9\). Use ((a-b)2 =a-2 -2ab+b-2 ). Here (a=2x) and (b=3).
Step 3
Exam Tip
((a-b)2 =a-2 -2ab+b-2 ) लगाएँ। यहाँ (a=2x) और (b=3) हैं।
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((3x+2)2 ) का विस्तार क्या है?
What is the expansion of ((3x+2)2 )?
#polynomials
#identity
#square of binomial
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A \(9x^2+12x+4\)
B \(9x^2+6x+4\)
C \(3x^2+12x+4\)
D \(9x^2+4\)
Explanation opens after your attempt
Correct Answer
A. \(9x^2+12x+4\)
Step 1
Concept
Take (a=3x) and (b=2) in ((a+b)2 ). The middle term is \(2\cdot3x\cdot2=12x\).
Step 2
Why this answer is correct
The correct answer is A. \(9x^2+12x+4\). Take (a=3x) and (b=2) in ((a+b)2 ). The middle term is \(2\cdot3x\cdot2=12x\).
Step 3
Exam Tip
((a+b)2 ) में (a=3x) और (b=2) लें। मध्य पद \(2\cdot3x\cdot2=12x\) है।
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((5x+4)(5x-4)) का सरल रूप क्या है?
What is the simplified form of ((5x+4)(5x-4))?
#polynomials
#difference of squares
#identity
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A \(25x^2-16\)
B \(25x^2+16\)
C (10x-16)
D \(25x^2-40x+16\)
Explanation opens after your attempt
Correct Answer
A. \(25x^2-16\)
Step 1
Concept
((a+b)(a-b)=a-2 -b-2 ). Here (a=5x) and (b=4).
Step 2
Why this answer is correct
The correct answer is A. \(25x^2-16\). ((a+b)(a-b)=a-2 -b-2 ). Here (a=5x) and (b=4).
Step 3
Exam Tip
((a+b)(a-b)=a-2 -b-2 ) है। यहाँ (a=5x) और (b=4) हैं।
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यदि \(2^x=32\) है तो (x) का मान क्या है?
If \(2^x=32\), what is the value of (x)?
#polynomials
#exponential equation
#basics
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A (4)
B (5)
C (6)
D (16)
Explanation opens after your attempt
Step 1
Concept
Since \(32=2^5\), \(2^x=2^5\) gives (x=5). Equal bases have equal exponents.
Step 2
Why this answer is correct
The correct answer is B. (5). Since \(32=2^5\), \(2^x=2^5\) gives (x=5). Equal bases have equal exponents.
Step 3
Exam Tip
क्योंकि \(32=2^5\), इसलिए \(2^x=2^5\) से (x=5)। समान आधार होने पर घातें बराबर होती हैं।
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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)?
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A (2)
B (3)
C (4)
D (5)
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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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(\frac{\(5^2\)3 }{54 \cdot5^{-1}}) का सरल रूप क्या है?
What is the simplified form of (\frac{\(5^2\)3 }{54 \cdot5^{-1}})?
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A \(5^3\)
B \(5^1\)
C \(5^9\)
D \(5^{-3}\)
Explanation opens after your attempt
Correct Answer
A. \(5^3\)
Step 1
Concept
First (\(5^2\)3 =56 ). The total exponent is (6-4-(-1)=3), so the answer is \(5^3\).
Step 2
Why this answer is correct
The correct answer is A. \(5^3\). First (\(5^2\)3 =56 ). The total exponent is (6-4-(-1)=3), so the answer is \(5^3\).
Step 3
Exam Tip
पहले (\(5^2\)3 =56 ) होता है। कुल घात (6-4-(-1)=3) है इसलिए उत्तर \(5^3\) है।
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(\frac{\(3x^2y^{-1}\)2 }{9xy^{-3}}) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of (\frac{\(3x^2y^{-1}\)2 }{9xy^{-3}}) if \(x\neq0\) and \(y\neq0\)?
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A \(x^3y\)
B \(x^3y^{-5}\)
C \(9x^3y\)
D \(x^4y\)
Explanation opens after your attempt
Correct Answer
A. \(x^3y\)
Step 1
Concept
The numerator is (\(3x^2y^{-1}\)2 =9x-4 y^{-2}). Dividing gives \(x^{4-1}y^{-2-(-3)}=x^3y\).
Step 2
Why this answer is correct
The correct answer is A. \(x^3y\). The numerator is (\(3x^2y^{-1}\)2 =9x-4 y^{-2}). Dividing gives \(x^{4-1}y^{-2-(-3)}=x^3y\).
Step 3
Exam Tip
ऊपर (\(3x^2y^{-1}\)2 =9x-4 y^{-2}) है। भाग देने पर \(x^{4-1}y^{-2-(-3)}=x^3y\) मिलता है।
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