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What is the simplified form of \(\left(\frac{27x^{-3}}{8y^{6}}\right)^{-\frac{1}{3}}\)?
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Answer and explanation
Correct answer: \(\frac{2xy^{2}}{3}\)
We get \(\left(\frac{27x^{-3}}{8y^{6}}\right)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}\), so the power \(-\frac{1}{3}\) gives its reciprocal \(\frac{2xy^{2}}{3}\). In exams, treat the negative fractional power as a reciprocal after rooting.
Frequently asked questions
What is the correct answer to this question?
\(\frac{2xy^{2}}{3}\)
Why is this the correct answer?
We get \(\left(\frac{27x^{-3}}{8y^{6}}\right)^{\frac{1}{3}}=\frac{3x^{-1}}{2y^{2}}\), so the power \(-\frac{1}{3}\) gives its reciprocal \(\frac{2xy^{2}}{3}\). In exams, treat the negative fractional power as a reciprocal after rooting.
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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