If \(a\neq0\) and \(b\neq0\), what is the simplified form of \(\left(\frac{a^{-2}}{b^{-4}}\right)^{-1}\)?
Answer and explanation
Correct answer: \(\frac{a^2}{b^4}\)
First, \(\frac{a^{-2}}{b^{-4}}=a^{-2}\times b^4=\frac{b^4}{a^2}\). Taking the power \(-1\) inverts the fraction: \(\left(\frac{b^4}{a^2}\right)^{-1}=\frac{a^2}{b^4}\). Therefore, option B is correct. Exam tip: the power \(-1\) of a non-zero number or fraction gives its reciprocal.
Frequently asked questions
What is the correct answer to this question?
\(\frac{a^2}{b^4}\)
Why is this the correct answer?
First, \(\frac{a^{-2}}{b^{-4}}=a^{-2}\times b^4=\frac{b^4}{a^2}\). Taking the power \(-1\) inverts the fraction: \(\left(\frac{b^4}{a^2}\right)^{-1}=\frac{a^2}{b^4}\). Therefore, option B is correct. Exam tip: the power \(-1\) of a non-zero number or fraction gives its reciprocal.
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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