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

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Answer and explanation

Correct answer: (5)

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

What is the correct answer to this question?

(5)

Why is this the correct answer?

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