What is the value of \(\left(49^{\frac{3}{2}}\right)\cdot\left(343^{-\frac{2}{3}}\right)\)?

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Correct answer: (1)

Here \(49^{\frac{3}{2}}=(7^{2})^{\frac{3}{2}}=7^{3}\) and \(343^{-\frac{2}{3}}=(7^{3})^{-\frac{2}{3}}=7^{-2}\). The product is \(7^{1}=7\).

What is the correct answer to this question?

(1)

Why is this the correct answer?

Here \(49^{\frac{3}{2}}=(7^{2})^{\frac{3}{2}}=7^{3}\) and \(343^{-\frac{2}{3}}=(7^{3})^{-\frac{2}{3}}=7^{-2}\). The product is \(7^{1}=7\).

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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