# How do you write sqrt(2^(5/8)) as a radical?

Jun 3, 2018

See a solution process below:

#### Explanation:

We can rewrite the expression as:

${\left({2}^{\frac{5}{8}}\right)}^{\frac{1}{2}}$

Next, we can use this rule of exponents to eliminate the outer exponent:

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

${\left({2}^{\textcolor{red}{\frac{5}{8}}}\right)}^{\textcolor{b l u e}{\frac{1}{2}}} \implies {2}^{\textcolor{red}{\frac{5}{8}} \times \textcolor{b l u e}{\frac{1}{2}}} \implies {2}^{\frac{5}{16}}$

Then, we can use the reverse of the rule above to rewrite the expression as:

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

${2}^{\textcolor{red}{5} \times \textcolor{b l u e}{\frac{1}{16}}} \implies {\left({2}^{\textcolor{red}{5}}\right)}^{\textcolor{b l u e}{\frac{1}{16}}} \implies {32}^{16} \implies \sqrt[16]{32}$