# What is radical form for 4^(1/3)?

Jun 12, 2016

$\sqrt[3]{4}$

#### Explanation:

We can write ${4}^{\frac{1}{3}}$ in radical form, but not with square roots. We can write this using cube roots.

Here is a quick differentiation:

$\sqrt{64} = 8 \mathmr{and} - 8$
$\sqrt[3]{64} = 4$

So, if we multiply $8$ or $- 8$ by itself, we get 64. If we multiply 4 by itself three times, we get 64. This same theory works with fraction exponents that get smaller (${x}^{\frac{1}{4}} , {x}^{\frac{1}{5}} , {x}^{\frac{1}{6}}$).

Anything written to the $\frac{1}{3}$ power is the cube root of that base number.

Given this, we can write:

${4}^{\frac{1}{3}}$ = $\sqrt[3]{4}$