# How do you write the expression (root4(5))^5 in exponential form?

Nov 3, 2017

See a solution process below:

#### Explanation:

First, use this rule for exponents to rewrite the radical:

$\sqrt[\textcolor{red}{n}]{x} = {x}^{\frac{1}{\textcolor{red}{n}}}$

${\left(\sqrt[\textcolor{red}{4}]{5}\right)}^{5} = {\left({5}^{\frac{1}{\textcolor{red}{4}}}\right)}^{5}$

Now, use this rule of exponents to combine the exponents:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({5}^{\textcolor{red}{\frac{1}{4}}}\right)}^{\textcolor{b l u e}{5}} = {5}^{\textcolor{red}{\frac{1}{4}} \times \textcolor{b l u e}{5}} = {5}^{\frac{5}{4}}$