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What is the simplified form of \(\left(\frac{125x^{-9}}{64y^{12}}\right)^{-\frac{1}{3}}\)?
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Answer and explanation
Correct answer: \(\frac{4x^{3}y^{4}}{5}\)
We get \(\left(\frac{125x^{-9}}{64y^{12}}\right)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}}\). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{4x^{3}y^{4}}{5}\).
Frequently asked questions
What is the correct answer to this question?
\(\frac{4x^{3}y^{4}}{5}\)
Why is this the correct answer?
We get \(\left(\frac{125x^{-9}}{64y^{12}}\right)^{\frac{1}{3}}=\frac{5x^{-3}}{4y^{4}}\). The power \(-\frac{1}{3}\) gives the reciprocal \(\frac{4x^{3}y^{4}}{5}\).
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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