# What is the cube root of x^8?

Oct 13, 2015

$\sqrt[3]{{x}^{8}} = {x}^{2} \sqrt[3]{{x}^{2}}$

or if you prefer:

$\sqrt[3]{{x}^{8}} = {x}^{\frac{8}{3}}$

#### Explanation:

For any $a , b \in \mathbb{R}$, $\sqrt[3]{a b} = \sqrt[3]{a} \sqrt[3]{b}$ and $\sqrt[3]{{a}^{3}} = a$

So:

$\sqrt[3]{{x}^{8}} = \sqrt[3]{{x}^{6} \cdot {x}^{2}} = \sqrt[3]{{\left({x}^{2}\right)}^{3} \cdot {x}^{2}} = \sqrt[3]{{\left({x}^{2}\right)}^{3}} \sqrt[3]{{x}^{2}} = {x}^{2} \sqrt[3]{{x}^{2}}$