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What is the simplified form of \(\left(\frac{x^{3}y^{-2}}{z^{-1}}\right)^{-1}\cdot\frac{x^{2}}{yz^{2}}\)?
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Answer and explanation
Correct answer: \(\frac{y}{xz}\)
Inside, \(\frac{x^{3}y^{-2}}{z^{-1}}=x^{3}y^{-2}z\), so its reciprocal is \(x^{-3}y^{2}z^{-1}\). Multiplying by \(\frac{x^{2}}{yz^{2}}\) gives \(\frac{y}{xz^{3}}\), so the (z)-power must be checked carefully.
Frequently asked questions
What is the correct answer to this question?
\(\frac{y}{xz}\)
Why is this the correct answer?
Inside, \(\frac{x^{3}y^{-2}}{z^{-1}}=x^{3}y^{-2}z\), so its reciprocal is \(x^{-3}y^{2}z^{-1}\). Multiplying by \(\frac{x^{2}}{yz^{2}}\) gives \(\frac{y}{xz^{3}}\), so the (z)-power must be checked carefully.
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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