# How do you simplify 4^(-1/2)?

Mar 6, 2017

See the entire simplification process below:

#### Explanation:

First, use this rule of exponents to write the expression:

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

${4}^{\textcolor{red}{- \frac{1}{2}}} = \frac{1}{4} ^ \textcolor{red}{- - \frac{1}{2}} = \frac{1}{4} ^ \textcolor{red}{\frac{1}{2}}$

Now use this rule of exponents and radicals to complete the simplification:

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

$\frac{1}{4} ^ \left(\frac{1}{\textcolor{red}{2}}\right) = \frac{1}{\sqrt[\textcolor{red}{2}]{4}} = \frac{1}{\sqrt{4}} = \frac{1}{2}$