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What is the value of \(\left(\frac{64}{125}\right)^{-\frac{2}{3}}\)?
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Answer and explanation
Correct answer: \(\frac{25}{16}\)
Since \(\left(\frac{64}{125}\right)^{\frac{1}{3}}=\frac{4}{5}\), \(\left(\frac{64}{125}\right)^{-\frac{2}{3}}=\left(\frac{4}{5}\right)^{-2}=\frac{25}{16}\). In exams, take the cube root first.
Frequently asked questions
What is the correct answer to this question?
\(\frac{25}{16}\)
Why is this the correct answer?
Since \(\left(\frac{64}{125}\right)^{\frac{1}{3}}=\frac{4}{5}\), \(\left(\frac{64}{125}\right)^{-\frac{2}{3}}=\left(\frac{4}{5}\right)^{-2}=\frac{25}{16}\). In exams, take the cube root first.
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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