# How do you evaluate and simplify 16^(3/2)?

Feb 3, 2017

See the entire solution process below:

#### Explanation:

First, we can use this rule of exponents to rewrite this expression:

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

${16}^{\frac{3}{2}} = {16}^{\textcolor{red}{\frac{1}{2}} \times \textcolor{b l u e}{3}} = {\left({16}^{\textcolor{red}{\frac{1}{2}}}\right)}^{\textcolor{b l u e}{3}}$

We can rewrite and simplify this as:

${\left({16}^{\textcolor{red}{\frac{1}{2}}}\right)}^{\textcolor{b l u e}{3}} = {\left(\sqrt{16}\right)}^{\textcolor{b l u e}{3}} = {4}^{\textcolor{b l u e}{3}}$

Now, we can simplify this to:
${4}^{\textcolor{b l u e}{3}} = 4 \times 4 \times 4 = 16 \times 4 = 64$