# How do you simplify (10^(1/3))^(1/2)?

Nov 4, 2015

The exact value of ${\left({10}^{\frac{1}{3}}\right)}^{\frac{1}{2}}$ is ${10}^{\frac{1}{6}}$ which is the sixth root of 10.

#### Explanation:

${\left({a}^{2}\right)}^{2}$ can be rewritten to ${a}^{4}$.

If it's hard to imagine, think of it like this:
${\left({a}^{2}\right)}^{2} = \left({a}^{2}\right) \cdot \left({a}^{2}\right) = a \cdot a \cdot a \cdot a$

${\left({10}^{\frac{1}{3}}\right)}^{\frac{1}{2}}$ = ${10}^{\frac{1}{3} \cdot \frac{1}{2}}$ = ${10}^{\frac{1}{6}}$