Question

Simplify $8^{\frac{2}{3}}$.

Answer 1

Use appropriate laws of exponents

We know that $8$ can be expressed in the power of $2$.

$$\begin{gathered} 8=2X2X2 \\ 8=2^3 \end{gathered}$$

Hence the given number becomes

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

$=$$2^{3\times \frac{2}{3}}$ $\left[\because {\left(a^m\right)}^n=a^{m\times n}\right]$

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

Hence, $8^{\frac{2}{3}}=4$