Question

How do you evaluate $32$ to the power of $\frac{2}{5}$?

Answer 1

Compute the required value:

According to the law of indices, $x^{\frac{p}{q}}=\sqrt[q]{x^p}$ which is equal to ${\left(\sqrt[q]{x}\right)}^p$.

So,

$\Rightarrow$${32}^{\frac{2}{5}}={\left(\sqrt[5]{32}\right)}^2$

$\Rightarrow$${\left(\sqrt[5]{2\times 2\times 2\times 2\times 2}\right)}^2$

$\Rightarrow$$2^2$

$\Rightarrow$${32}^{\frac{2}{5}}=4$

Hence the required value of ${32}^{\frac{2}{5}}$ is $4$.