If \(x\ne0\) and \(y\ne0\), what is the simplified form of \(\left(\frac{x^{-3}}{y^{-2}}\right)^{-1}\)?
Answer and explanation
Correct answer: \(\frac{x^3}{y^2}\)
First, \(\frac{x^{-3}}{y^{-2}}=x^{-3}\times y^2=\frac{y^2}{x^3}\). Applying the outer power \(-1\) takes the reciprocal: \(\left(\frac{y^2}{x^3}\right)^{-1}=\frac{x^3}{y^2}\). Therefore, option A is correct. Option B is only the simplified inner expression and does not include the effect of the outer \(-1\) power. Exam tip: the \(-1\) power of any nonzero expression gives its reciprocal.
Frequently asked questions
What is the correct answer to this question?
\(\frac{x^3}{y^2}\)
Why is this the correct answer?
First, \(\frac{x^{-3}}{y^{-2}}=x^{-3}\times y^2=\frac{y^2}{x^3}\). Applying the outer power \(-1\) takes the reciprocal: \(\left(\frac{y^2}{x^3}\right)^{-1}=\frac{x^3}{y^2}\). Therefore, option A is correct. Option B is only the simplified inner expression and does not include the effect of the outer \(-1\) power. Exam tip: the \(-1\) power of any nonzero expression 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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