# How do you simplify 5/3rd root of 26^2?

Oct 9, 2015

$\sqrt[\frac{5}{3}]{{26}^{2}} = {\left({26}^{2}\right)}^{\frac{3}{5}} = {26}^{\frac{6}{5}}$

#### Explanation:

The $n$th root of a number $a$ is ${a}^{\frac{1}{n}}$

So the $\frac{5}{3}$rd root of a number $a$ is ${a}^{\frac{3}{5}}$

In addtion, if $a > 0$ and $b , c \ne 0$, then ${\left({a}^{b}\right)}^{c} = {a}^{b c}$

So:

$\sqrt[\frac{5}{3}]{{26}^{2}} = {\left({26}^{2}\right)}^{\frac{3}{5}} = {26}^{2 \cdot \frac{3}{5}} = {26}^{\frac{6}{5}}$

This cannot be simplified further since $26$ has no fifth power factors.