# How do you write with fractional exponents 1/5(sqrt x^2)?

Aug 2, 2015

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

#### Explanation:

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

But ${\left({x}^{a}\right)}^{b} = {x}^{a b}$, so

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

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