# How do you simplify sqrt (x^5)?

Aug 29, 2016

${x}^{\frac{5}{2}}$

#### Explanation:

The only way this may be simplified is by expressing as a fractional exponent.

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\sqrt{x} = {x}^{\frac{1}{2}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \sqrt{{x}^{5}} = {\left({x}^{5}\right)}^{\frac{1}{2}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{\left({a}^{m}\right)}^{n} = {a}^{m n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow {\left({x}^{5}\right)}^{\frac{1}{2}} = {x}^{5 \times \frac{1}{2}} = {x}^{\frac{5}{2}}$

$\Rightarrow \sqrt{{x}^{5}} = {x}^{\frac{5}{2}}$