# How do you write root5(2^8) as a radical?

Aug 2, 2017

See a solution process below:

#### Explanation:

This is already written as a radical. However, we can simplify this term by rewriting the term under the radical and then using this rule of radicals:

$\sqrt[n]{\textcolor{red}{a}} \cdot \sqrt[n]{\textcolor{b l u e}{b}} = \sqrt[n]{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}}$

$\sqrt[5]{{2}^{8}} \implies \sqrt[5]{\textcolor{red}{{2}^{5}} \cdot \textcolor{b l u e}{{2}^{3}}} = \sqrt[5]{\textcolor{red}{{2}^{5}}} \cdot \sqrt[5]{\textcolor{b l u e}{{2}^{3}}} \implies 2 \sqrt[5]{\textcolor{b l u e}{{2}^{3}}}$

If necessary, this can be rewritten as:

$2 \sqrt[5]{8}$