# How do you write (-28)^(7/5) in radical form?

Jun 6, 2017

${\left(\sqrt[5]{- 28}\right)}^{7}$

#### Explanation:

${m}^{\frac{1}{n}} \equiv \sqrt[n]{m}$

${\left(- 28\right)}^{\frac{5}{7}}$

$= {\left({\left(- 28\right)}^{\frac{1}{5}}\right)}^{7}$

$= {\left(\sqrt[5]{- 28}\right)}^{7}$

Jun 6, 2017

See a solution process below:

#### Explanation:

We can rewrite this expression as:

${\left(- 28\right)}^{7 \times \frac{1}{5}}$

We can now use this rule of exponents to rewrite the expression again:

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

${\left(- 28\right)}^{\textcolor{red}{7} \times \textcolor{b l u e}{\frac{1}{5}}} = {\left(- {28}^{\textcolor{red}{7}}\right)}^{\textcolor{b l u e}{\frac{1}{5}}}$

We can now use this rule for exponents and radicals to put the expression into radical form:

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

${\left(- {28}^{7}\right)}^{\frac{1}{\textcolor{red}{5}}} = \sqrt[\textcolor{red}{5}]{- {28}^{7}}$