# How do you write 21^(9/4) in radical notation?

Jan 7, 2017

${\sqrt[4]{21}}^{9}$

or

$441 \sqrt[4]{21}$

#### Explanation:

Since ${a}^{\frac{m}{n}} = {\sqrt[n]{a}}^{m}$

you get:

${21}^{\frac{9}{4}} = {\sqrt[4]{21}}^{9}$

or

${21}^{2} \sqrt[4]{21} = 441 \sqrt[4]{21}$

Jan 7, 2017

See full explanation below:

#### Explanation:

We can use the following rule for exponents to rewrite this expression:

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

${21}^{\frac{9}{4}} \to {\left({21}^{9}\right)}^{\frac{1}{4}}$

The next rule for exponents we need to employ to get this into radical notation is:

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

${\left({21}^{9}\right)}^{\frac{1}{\textcolor{red}{4}}} \to$

$\sqrt[\textcolor{red}{4}]{{21}^{9}}$