How do you simplify 8^(2/6)?

Jan 26, 2017

$2$

Explanation:

The first point to note is that.

$\frac{2}{6} = \frac{1}{3} \leftarrow \textcolor{red}{\text{ in simplest form}}$

$\Rightarrow {8}^{\frac{2}{6}} = {8}^{\frac{1}{3}}$

Using the $\textcolor{b l u e}{\text{law of exponents}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{a}^{\frac{m}{n}} = {\left(\sqrt[n]{a}\right)}^{m}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {8}^{\frac{1}{3}} = \sqrt[3]{8} = 2$