Question

Simplify: ${64}^{\frac{1}{2}}$

Answer 1

Consider ${64}^{\frac{1}{2}}$

but $64=8^2$

$$\begin{gathered} \therefore {64}^{\frac{1}{2}} \\ {\left(8^2\right)}^{\frac{1}{2}} \end{gathered}$$

We know that ${\left(a^m\right)}^n=a^{m\times n}$

$$\begin{gathered} 8^{2\times \frac{1}{2}} \\ {8}^{\frac{2}{2}} \\ {8}^1 \\ 8 \end{gathered}$$

Hence, ${64}^{\frac{1}{2}}$ is $8$