# How do you simplify 2^(1/4) * 8^(1/4)?

Mar 11, 2018

The simplified expression is $2$.

#### Explanation:

Use these exponent rules to simplify the expression:

${x}^{\textcolor{red}{m}} + {x}^{\textcolor{b l u e}{n}} = {x}^{\textcolor{red}{m} + \textcolor{b l u e}{n}}$

${\left({x}^{\textcolor{red}{m}}\right)}^{\textcolor{b l u e}{n}} = {x}^{\textcolor{red}{m} \cdot \textcolor{b l u e}{n}}$

Now here's the expression. Rewrite $8$ as ${2}^{3}$, then use the exponent rules to simplify:

$\textcolor{w h i t e}{=} {2}^{\frac{1}{4}} \cdot {8}^{\frac{1}{4}}$

$= {2}^{\textcolor{g r e e n}{\frac{1}{4}}} \cdot {\left({2}^{\textcolor{red}{3}}\right)}^{\textcolor{b l u e}{\frac{1}{4}}}$

$= {2}^{\textcolor{g r e e n}{\frac{1}{4}}} \cdot {2}^{\textcolor{red}{3} \cdot \textcolor{b l u e}{\frac{1}{4}}}$

=2^color(green)(1/4)*2^(color(blue)(color(red)3/4)

$= {2}^{\textcolor{g r e e n}{\frac{1}{4}} + \textcolor{b l u e}{\frac{\textcolor{red}{3}}{4}}}$

$= {2}^{\textcolor{b l u e}{\frac{\textcolor{g r e e n}{1} \textcolor{b l a c k}{+} \textcolor{red}{3}}{4}}}$

=2^(color(blue)(color(brown)4/4)

$= {2}^{1}$

$= 2$

Mar 11, 2018

$\pm 2$

#### Explanation:

${2}^{\frac{1}{4}} \cdot {8}^{\frac{1}{4}}$
$\textcolor{w h i t e}{\text{XXX}} = {\left(2 \cdot 8\right)}^{\frac{1}{4}}$
$\textcolor{w h i t e}{\text{XXX}} = {16}^{\frac{1}{4}}$
$\textcolor{w h i t e}{\text{XXX}} = \pm \sqrt[4]{16}$
$\textcolor{w h i t e}{\text{XXX}} = \pm 2$