# How do you write y^(5/4) in radical form?

Mar 11, 2018

${y}^{\frac{5}{4}} = \sqrt[4]{{y}^{5}}$

#### Explanation:

${y}^{\frac{x}{n}} = \sqrt[n]{{y}^{x}}$

${y}^{\frac{5}{4}} = \sqrt[4]{{y}^{5}}$

Mar 11, 2018

See a solution process below:

#### Explanation:

First, rewrite the exponent as:

${y}^{5 \cdot \frac{1}{4}}$

Then use this rule of exponents to rewrite the expression:

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

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

Then use this rule of exponents and radicals to write the expression in radical form:

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

If you want to simplify this expression we can use this rule for radicals:

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

$\sqrt[4]{{y}^{5}} \implies \sqrt[4]{\textcolor{red}{{y}^{4}} \cdot \textcolor{b l u e}{y}} = \sqrt[4]{\textcolor{red}{{y}^{4}}} \cdot \sqrt[4]{\textcolor{b l u e}{y}} \implies y \sqrt[4]{y}$