# How do you write (5x)^(2/5) in radical form?

Apr 24, 2017

See the entire solution process below:

#### Explanation:

First, we can use this rule of exponents to rewrite this expression:

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

${\left(5 x\right)}^{\frac{2}{5}} = {\left(5 x\right)}^{\textcolor{red}{2} \times \textcolor{b l u e}{\frac{1}{5}}} = {\left({\left(5 x\right)}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{\frac{1}{5}}}$

We can now use these rules for exponents to rewrite the term within the parenthesis:

$a = {a}^{\textcolor{red}{1}}$ and the reverse of the rule we used above: ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({\left(5 x\right)}^{2}\right)}^{\frac{1}{5}} = {\left({\left({5}^{\textcolor{red}{1}} {x}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{2}}\right)}^{\frac{1}{5}} = {\left({5}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {x}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}}\right)}^{\frac{1}{5}} = {\left({5}^{2} {x}^{2}\right)}^{\frac{1}{5}} = {\left(25 {x}^{2}\right)}^{\frac{1}{5}}$

We can now use this rule of exponents and radicals to write the expression in radical form:

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

${\left(25 {x}^{2}\right)}^{\frac{1}{\textcolor{red}{5}}} = \sqrt[\textcolor{red}{5}]{25 {x}^{2}}$