Question

Find: ${32}^{\frac{2}{5}}$.

Answer 1

Compute the required value.

First, we can write the number $32$ as

$$\begin{gathered} 32=2\times 2\times 2\times 2\times 2 \\ =2^5 \end{gathered}$$

That is

$$\begin{gathered} {32}^{\frac{2}{5}}={\left(2^5\right)}^{\frac{2}{5}} \\ =2^{5\times \frac{2}{5}} \end{gathered}$$

$$\begin{gathered} =2^2 \\ =4 \end{gathered}$$

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