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Which of the following statements is true for all non-zero real numbers \(a\) and \(b\), according to the laws of exponents?
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Answer and explanation
Correct answer: \((ab)^{-1}=a^{-1}b^{-1}\)
A negative exponent represents a reciprocal. Thus, \((ab)^{-1}=\frac{1}{ab}=\frac{1}{a}\cdot\frac{1}{b}=a^{-1}b^{-1}\). No similar rule applies to a sum or difference. Exam tip: distinguish a product from a sum before using exponent laws.
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What is the correct answer to this question?
\((ab)^{-1}=a^{-1}b^{-1}\)
Why is this the correct answer?
A negative exponent represents a reciprocal. Thus, \((ab)^{-1}=\frac{1}{ab}=\frac{1}{a}\cdot\frac{1}{b}=a^{-1}b^{-1}\). No similar rule applies to a sum or difference. Exam tip: distinguish a product from a sum before using exponent laws.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.
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