# How do you simplify root4(x^16)?

Jul 4, 2018

Simplifying this root gives us ${x}^{4}$

#### Explanation:

So you can think of this as how many group of 4 can make 16.

So what gives us ${x}^{16}$? The answer is 4 because 4 x 4 = 16.

Jul 4, 2018

${x}^{4}$

#### Explanation:

We can rewrite the monomial under the radical

${\left({x}^{4}\right)}^{4}$, which allows us to rewrite the entire expression as

$\sqrt[\textcolor{b l u e}{4}]{{\left({x}^{4}\right)}^{\textcolor{b l u e}{4}}}$

The fourth root cancels with the fourth power, and we're left with

${x}^{4}$

Hope this helps!