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What is the simplified form of \(\left(\frac{x^{-2}y^{4}}{z^{-3}}\right)^{-1}\cdot\frac{y^{2}}{x^{3}z^{2}}\)?
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Answer and explanation
Correct answer: \(\frac{z}{xy^{2}}\)
Inside, \(\frac{x^{-2}y^{4}}{z^{-3}}=x^{-2}y^{4}z^{3}\), so its reciprocal is \(x^{2}y^{-4}z^{-3}\). Multiplying by \(\frac{y^{2}}{x^{3}z^{2}}\) gives \(\frac{1}{xy^{2}z^{5}}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{z}{xy^{2}}\)
Why is this the correct answer?
Inside, \(\frac{x^{-2}y^{4}}{z^{-3}}=x^{-2}y^{4}z^{3}\), so its reciprocal is \(x^{2}y^{-4}z^{-3}\). Multiplying by \(\frac{y^{2}}{x^{3}z^{2}}\) gives \(\frac{1}{xy^{2}z^{5}}\).
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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