# How do you simplify 2^sqrt7*2^sqrt7?

##### 2 Answers
Mar 10, 2018

Simplified, the expression is ${4}^{\sqrt{7}}$.

#### Explanation:

Use these exponent rules to simplify the expression:

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

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

Now here's the actual problem:

$\textcolor{w h i t e}{=} {2}^{\textcolor{red}{\sqrt{7}}} \cdot {2}^{\textcolor{b l u e}{\sqrt{7}}}$

$= {2}^{\textcolor{red}{\sqrt{7}} + \textcolor{b l u e}{\sqrt{7}}}$

$= {2}^{\textcolor{p u r p \le}{2 \sqrt{7}}}$

$= {2}^{2 \cdot \textcolor{p u r p \le}{\sqrt{7}}}$

$= {\left({2}^{2}\right)}^{\textcolor{p u r p \le}{\sqrt{7}}}$

$= {4}^{\textcolor{p u r p \le}{\sqrt{7}}} \approx 39.16525 \ldots$

That's as simplified as it gets, unfortunately.

Mar 10, 2018

${4}^{7} = 16384$

#### Explanation:

${2}^{\sqrt{7}} \cdot {2}^{\sqrt{7}}$
$2 \cdot 2 = 4$
${1}^{\sqrt{7}} \cdot {1}^{\sqrt{7}} = {1}^{7}$
$4 \cdot {1}^{7} = {4}^{7}$
$4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 \cdot 4 = {4}^{7} = 16384$