What is the value of \(\left(125^{\frac{2}{3}}\right)\cdot\left(25^{-\frac{3}{2}}\right)\)?

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Answer and explanation

Correct answer: \(\frac{1}{5}\)

Here \(125^{\frac{2}{3}}=(5)^{2}=25\) and \(25^{-\frac{3}{2}}=(5)^{-3}=\frac{1}{125}\). The product is \(\frac{1}{5}\).

What is the correct answer to this question?

\(\frac{1}{5}\)

Why is this the correct answer?

Here \(125^{\frac{2}{3}}=(5)^{2}=25\) and \(25^{-\frac{3}{2}}=(5)^{-3}=\frac{1}{125}\). The product is \(\frac{1}{5}\).

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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