Question

How do you simplify $8^{\frac{2}{3}}$?

Answer 1

Step-1: Simplify the expression:

Given that, $8^{\frac{2}{3}}$

Rewrite ${\displaystyle 8}$ as ${\displaystyle 2^3}$:

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

Step-2: Apply the power rule:

Use the power rule ${\displaystyle {\left(a^m\right)}^n=a^{mn}}$ and multiply the exponents:

$\begin{array}{rcl}{8}^{\frac{2}{3}}& =& {\left(2^3\right)}^{\frac{2}{3}}\\ & =& {\left(2\right)}^{3\times \frac{2}{3}}[\therefore {\left(a^m\right)}^n=a^{mn}]\\ & =& {\left(2\right)}^2[\mathrm{cancel}\mathrm{the}\mathrm{terms}]\\ & =& 4\end{array}$

Hence, the simplification of the term ${\mathbf{8}}^{\frac{\mathbf{2}}{\mathbf{3}}}$is $\mathbf{4}$.