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What is the simplified form of \(\left(\frac{x^{-4}y^{5}}{z^{-2}}\right)^{-1}\cdot\frac{y^{3}}{x^{2}z^{4}}\)?
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Answer and explanation
Correct answer: \(\frac{x^{2}}{y^{2}z^{2}}\)
Inside, \(\frac{x^{-4}y^{5}}{z^{-2}}=x^{-4}y^{5}z^{2}\), so its reciprocal is \(x^{4}y^{-5}z^{-2}\). Multiplying by \(\frac{y^{3}}{x^{2}z^{4}}\) gives \(\frac{x^{2}}{y^{2}z^{6}}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{x^{2}}{y^{2}z^{2}}\)
Why is this the correct answer?
Inside, \(\frac{x^{-4}y^{5}}{z^{-2}}=x^{-4}y^{5}z^{2}\), so its reciprocal is \(x^{4}y^{-5}z^{-2}\). Multiplying by \(\frac{y^{3}}{x^{2}z^{4}}\) gives \(\frac{x^{2}}{y^{2}z^{6}}\).
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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