# How do you write root4(2^6) as a radical?

Jun 11, 2017

See a possible solution process below:

#### Explanation:

This expression is already written as a radical. If you want to simplify this expression we can use the following process:

$\sqrt[4]{{2}^{6}} = \sqrt[4]{{2}^{4} \cdot {2}^{2}} = \sqrt[4]{{2}^{4}} \cdot \sqrt[4]{{2}^{2}} = 2 \cdot \sqrt[4]{4} = 2 \sqrt[4]{4}$

If you want to write this expression using exponents you can use this rule of radicals and exponents to rewrite this expression:

$\sqrt[\textcolor{red}{n}]{x} = {x}^{\frac{1}{\textcolor{red}{n}}}$

$\sqrt[\textcolor{red}{4}]{{2}^{6}} = \left({2}^{6}\right) {x}^{\frac{1}{\textcolor{red}{4}}}$

We can now use this rule of exponents to simplify the expression:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left({2}^{\textcolor{red}{6}}\right)}^{\textcolor{b l u e}{\frac{1}{4}}} = {2}^{\textcolor{red}{6} \times \textcolor{b l u e}{\frac{1}{4}}} = {2}^{\frac{6}{4}} = {2}^{\frac{3}{2}}$