# How do you solve  x^(2/3)=(1/8)?

Jan 10, 2016

Start by raising both sides of the equation to the $\frac{3}{2}$ power ...

#### Explanation:

${x}^{\frac{2}{3}} = \left(\frac{1}{8}\right)$

${\left[{x}^{\frac{2}{3}}\right]}^{\frac{3}{2}} = {\left[\left(\frac{1}{8}\right)\right]}^{\frac{3}{2}}$

Now simplify ...

$x = \pm \frac{1}{\sqrt{{8}^{3}}} = \pm \frac{1}{16 \sqrt{2}} = \pm \frac{\sqrt{2}}{32}$

hope that helped