Question

How do you simplify ${\left(8\right)}^{\frac{2}{3}}$?

Answer 1

Evaluating ${\left(8\right)}^{\frac{2}{3}}$:

$$\begin{gathered} ={\left(8\right)}^{\frac{2}{3}} \\ =\sqrt[3]{{\left(8\right)}^2}\left[\because a^{\frac{m}{n}}=\sqrt[n]{a^m}\right] \\ =\sqrt[3]{64} \\ =\sqrt[3]{4\times 4\times 4} \\ =4 \end{gathered}$$

Therefore, ${\left(8\right)}^{\frac{2}{3}}=4$.