(\frac{\(2^4\)2 \cdot8^{-1}}{4}) का सरल रूप क्या है?
What is the simplified form of (\frac{\(2^4\)2 \cdot8^{-1}}{4})?
#polynomials
#exponent laws
#simplification
A \(2^3\)
B \(2^4\)
C \(2^5\)
D \(2^6\)
Explanation opens after your attempt
Correct Answer
A. \(2^3\)
Step 1
Concept
(\(2^4\)2 =28 ), \(8^{-1}=2^{-3}\), and \(4=2^2\). The total exponent is (8-3-2=3).
Step 2
Why this answer is correct
The correct answer is A. \(2^3\). (\(2^4\)2 =28 ), \(8^{-1}=2^{-3}\), and \(4=2^2\). The total exponent is (8-3-2=3).
Step 3
Exam Tip
(\(2^4\)2 =28 ), \(8^{-1}=2^{-3}\) और \(4=2^2\) है। कुल घात (8-3-2=3) है।
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\(\frac{18x^5y^3}{6x^2y}\) का सरल रूप क्या है यदि \(x\neq0\) और \(y\neq0\)?
What is the simplified form of \(\frac{18x^5y^3}{6x^2y}\) if \(x\neq0\) and \(y\neq0\)?
#polynomials
#monomial division
#exponent laws
A \(3x^3y^2\)
B \(12x^3y^2\)
C \(3x^7y^4\)
D \(108x^3y^2\)
Explanation opens after your attempt
Correct Answer
A. \(3x^3y^2\)
Step 1
Concept
The coefficient is \(\frac{18}{6}=3\), \(x^{5-2}=x^3\), and \(y^{3-1}=y^2\). So the answer is \(3x^3y^2\).
Step 2
Why this answer is correct
The correct answer is A. \(3x^3y^2\). The coefficient is \(\frac{18}{6}=3\), \(x^{5-2}=x^3\), and \(y^{3-1}=y^2\). So the answer is \(3x^3y^2\).
Step 3
Exam Tip
गुणांक \(\frac{18}{6}=3\), \(x^{5-2}=x^3\) और \(y^{3-1}=y^2\) है। इसलिए उत्तर \(3x^3y^2\) है।
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(\frac{\(3^2\)4 }{35 \cdot3^{-2}}) का सरल रूप क्या है?
What is the simplified form of (\frac{\(3^2\)4 }{35 \cdot3^{-2}})?
#polynomials
#exponent laws
#simplification
A \(3^5\)
B \(3^3\)
C \(3^{-1}\)
D \(3^{15}\)
Explanation opens after your attempt
Correct Answer
A. \(3^5\)
Step 1
Concept
First (\(3^2\)4 =38 ) and the denominator exponent is (5-2=3). Therefore the total exponent is (8-3=5).
Step 2
Why this answer is correct
The correct answer is A. \(3^5\). First (\(3^2\)4 =38 ) and the denominator exponent is (5-2=3). Therefore the total exponent is (8-3=5).
Step 3
Exam Tip
पहले (\(3^2\)4 =38 ) और हर की घात (5-2=3) है। इसलिए कुल घात (8-3=5) होती है।
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(\frac{\(2^3\)2 \cdot4^{-1}}{8}) का सरल रूप क्या है?
What is the simplified form of (\frac{\(2^3\)2 \cdot4^{-1}}{8})?
#polynomials
#exponent laws
#simplification
A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(\(2^3\)2 =26 ), \(4^{-1}=2^{-2}\), and \(8=2^3\). The total exponent is (6-2-3=1), so the answer is (2).
Step 2
Why this answer is correct
The correct answer is A. (2). (\(2^3\)2 =26 ), \(4^{-1}=2^{-2}\), and \(8=2^3\). The total exponent is (6-2-3=1), so the answer is (2).
Step 3
Exam Tip
(\(2^3\)2 =26 ), \(4^{-1}=2^{-2}\) और \(8=2^3\) है। कुल घात (6-2-3=1) है इसलिए उत्तर (2) है।
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\(24a^5b^3\div6a^2b^2\) का सरल रूप क्या है यदि \(a\neq0\) और \(b\neq0\)?
What is the simplified form of \(24a^5b^3\div6a^2b^2\) if \(a\neq0\) and \(b\neq0\)?
#polynomials
#monomial division
#exponent laws
A \(4a^3b\)
B \(18a^3b\)
C \(4a^7b^5\)
D \(144a^3b\)
Explanation opens after your attempt
Correct Answer
A. \(4a^3b\)
Step 1
Concept
The coefficient is \(\frac{24}{6}=4\), \(a^{5-2}=a^3\), and \(b^{3-2}=b\). So the answer is \(4a^3b\).
Step 2
Why this answer is correct
The correct answer is A. \(4a^3b\). The coefficient is \(\frac{24}{6}=4\), \(a^{5-2}=a^3\), and \(b^{3-2}=b\). So the answer is \(4a^3b\).
Step 3
Exam Tip
गुणांक \(\frac{24}{6}=4\), \(a^{5-2}=a^3\) और \(b^{3-2}=b\) है। इसलिए उत्तर \(4a^3b\) 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}})?
#polynomials
#exponent laws
#negative exponent
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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\(15a^4b^2\div5a^2b\) 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
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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\(\frac{2^3\cdot4^3}{8^2}\) का सरल रूप क्या है?
What is the simplified form of \(\frac{2^3\cdot4^3}{8^2}\)?
#polynomials
#exponent laws
#simplification
A \(2^3\)
B \(2^4\)
C \(2^5\)
D \(2^6\)
Explanation opens after your attempt
Correct Answer
C. \(2^5\)
Step 1
Concept
First write (43 =\(2^2\)3 =26 ) and (82 =\(2^3\)2 =26 ). Thus \(\frac{2^3\cdot2^6}{2^6}=2^{3+6-6}=2^3\), so the correct option is \(2^3\).
Step 2
Why this answer is correct
The correct answer is C. \(2^5\). First write (43 =\(2^2\)3 =26 ) and (82 =\(2^3\)2 =26 ). Thus \(\frac{2^3\cdot2^6}{2^6}=2^{3+6-6}=2^3\), so the correct option is \(2^3\).
Step 3
Exam Tip
पहले (43 =\(2^2\)3 =26 ) और (82 =\(2^3\)2 =26 ) लिखें। इसलिए \(\frac{2^3\cdot2^6}{2^6}=2^3\) नहीं बल्कि \(2^{3+6-6}=2^3\); सही विकल्प \(2^3\) है।
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कौन सा नियम सही है?
Which law is correct?
#polynomials
#exponent laws
#formula
A \(c^m\cdot c^n=c^{m+n}\)
B \(c^m\cdot c^n=c^{m-n}\)
C \(c^m\cdot c^n=c^{mn}\)
D (c^m\cdot c^n=c^{m / n})
Explanation opens after your attempt
Correct Answer
A. \(c^m\cdot c^n=c^{m+n}\)
Step 1
Concept
In multiplication with the same base, exponents are added. So \(c^m\cdot c^n=c^{m+n}\) is the correct law.
Step 2
Why this answer is correct
The correct answer is A. \(c^m\cdot c^n=c^{m+n}\). In multiplication with the same base, exponents are added. So \(c^m\cdot c^n=c^{m+n}\) is the correct law.
Step 3
Exam Tip
समान आधार के गुणन में घातें जुड़ती हैं। इसलिए \(c^m\cdot c^n=c^{m+n}\) सही नियम है।
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(\(a^m\)^n) किसके बराबर है?
What is (\(a^m\)^n) equal to?
#polynomials
#exponent laws
#power of power
A \(a^{m+n}\)
B \(a^{m-n}\)
C \(a^{mn}\)
D (a^{m / n})
Explanation opens after your attempt
Correct Answer
C. \(a^{mn}\)
Step 1
Concept
In a power of a power, exponents are multiplied. Therefore (\(a^m\)^n=a^{mn}) is correct.
Step 2
Why this answer is correct
The correct answer is C. \(a^{mn}\). In a power of a power, exponents are multiplied. Therefore (\(a^m\)^n=a^{mn}) is correct.
Step 3
Exam Tip
घात की घात में घातों का गुणा होता है। इसलिए (\(a^m\)^n=a^{mn}) सही है।
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यदि \(a\neq0\) है तो \(\frac{a^m}{a^n}\) किसके बराबर है?
If \(a\neq0\), what is \(\frac{a^m}{a^n}\) equal to?
#polynomials
#exponent laws
#quotient formula
A \(a^{m+n}\)
B \(a^{m-n}\)
C \(a^{mn}\)
D \(a^{n-m}\)
Explanation opens after your attempt
Correct Answer
B. \(a^{m-n}\)
Step 1
Concept
In division with the same base, exponents are subtracted, so \(\frac{a^m}{a^n}=a^{m-n}\). The condition \(a\neq0\) is important.
Step 2
Why this answer is correct
The correct answer is B. \(a^{m-n}\). In division with the same base, exponents are subtracted, so \(\frac{a^m}{a^n}=a^{m-n}\). The condition \(a\neq0\) is important.
Step 3
Exam Tip
समान आधार के भाग में घातें घटती हैं इसलिए \(\frac{a^m}{a^n}=a^{m-n}\)। शर्त \(a\neq0\) जरूरी है।
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यदि \(a=2^6\times3^4\times5^2\) और \(b=2^2\times3\times5\), तो \(\frac{a}{b}\) का अभाज्य गुणनखंड रूप क्या होगा?
If \(a=2^6\times3^4\times5^2\) and \(b=2^2\times3\times5\), what is the prime factorised form of \(\frac{a}{b}\)?
#real numbers
#division
#prime factorisation
#exponent laws
A \(2^4\times3^3\times5\)
B \(2^8\times3^5\times5^3\)
C \(2^3\times3^4\times5\)
D \(2^4\times3\times5^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^4\times3^3\times5\)
Step 1
Concept
When dividing powers with the same base, subtract exponents.
Step 2
Why this answer is correct
\(2^{6-2}\times3^{4-1}\times5^{2-1}=2^4\times3^3\times5\).
Step 3
Exam Tip
In division, subtract the smaller exponent from the larger one. चरण 1: समान आधारों को भाग देते समय घातें घटती हैं। चरण 2: \(2^{6-2}\times3^{4-1}\times5^{2-1}=2^4\times3^3\times5\)। चरण 3: भाग में बड़ी घात से छोटी घात घटाएं।
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यदि \(a=2^3\times3\times5\) और \(b=2^2\times3^2\times5^2\), तो \(a\times b\) का अभाज्य गुणनखंड रूप क्या होगा?
If \(a=2^3\times3\times5\) and \(b=2^2\times3^2\times5^2\), what is the prime factorised form of \(a\times b\)?
#real numbers
#exponent laws
#prime factorisation
#product
A \(2^5\times3^3\times5^3\)
B \(2^6\times3^2\times5^2\)
C \(2^5\times3^2\times5^2\)
D \(2\times3\times5\)
Explanation opens after your attempt
Correct Answer
A. \(2^5\times3^3\times5^3\)
Step 1
Concept
When multiplying powers with the same prime base, add exponents.
Step 2
Why this answer is correct
\(2^{3+2}\times3^{1+2}\times5^{1+2}=2^5\times3^3\times5^3\).
Step 3
Exam Tip
Add exponents for multiplication with the same base. चरण 1: समान आधार वाली अभाज्य घातों को गुणा करते समय घातें जोड़ी जाती हैं। चरण 2: \(2^{3+2}\times3^{1+2}\times5^{1+2}=2^5\times3^3\times5^3\)। चरण 3: आधार समान हो तो गुणा में घात जोड़ें, गुणा न करें।
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यदि दो संख्याओं का महत्तम समापवर्तक \(2^2\times3\) और लघुत्तम समापवर्त्य \(2^5\times3^3\times5\) है, तो उनके गुणनफल का अभाज्य रूप क्या होगा?
If the HCF of two numbers is \(2^2\times3\) and their LCM is \(2^5\times3^3\times5\), what is the prime factorised form of their product?
#real numbers
#hcf lcm product
#prime factorisation
#exponent laws
A \(2^7\times3^4\times5\)
B \(2^3\times3^2\times5\)
C \(2^{10}\times3^9\times5^2\)
D \(2^5\times3^3\times5\)
Explanation opens after your attempt
Correct Answer
A. \(2^7\times3^4\times5\)
Step 1
Concept
Product of two numbers equals HCF multiplied by LCM.
Step 2
Why this answer is correct
Multiply \(2^2\times3\) with \(2^5\times3^3\times5\); add exponents to get \(2^7\times3^4\times5\).
Step 3
Exam Tip
When multiplying same bases, add exponents. चरण 1: दो संख्याओं का गुणनफल उनके महत्तम समापवर्तक और लघुत्तम समापवर्त्य के गुणनफल के बराबर होता है। चरण 2: \(2^2\times3\) और \(2^5\times3^3\times5\) को गुणा करने पर घातें जुड़ती हैं, इसलिए \(2^7\times3^4\times5\)। चरण 3: समान आधारों को गुणा करते समय घातें जोड़ें।
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