How do you simplify $2^{\sqrt{7}} \cdot 2^{\sqrt{7}}$ $2^sqrt7*2^sqrt7$ ?

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Answer 1 · 2018-03-10T20:15:02

Simplified, the expression is $4^{\sqrt{7}}$ $4^sqrt7$ .

Use these exponent rules to simplify the expression:

$x^{m} \cdot x^{n} = x^{m + n}$ $x^color(red)m*x^color(blue)n=x^(color(red)m+color(blue)n)$

${(x^{m})}^{n} = x^{m \cdot n}$ $(x^color(red)m)^color(blue)n=x^(color(red)m*color(blue)n)$

Now here's the actual problem:

$= 2^{\sqrt{7}} \cdot 2^{\sqrt{7}}$ $color(white)=2^color(red)sqrt7*2^color(blue)sqrt7$

$= 2^{\sqrt{7} + \sqrt{7}}$ $=2^(color(red)sqrt7+color(blue)sqrt7)$

$= 2^{2 \sqrt{7}}$ $=2^(color(purple)(2sqrt7))$

$= 2^{2 \cdot \sqrt{7}}$ $=2^(2*color(purple)sqrt7)$

$= {(2^{2})}^{\sqrt{7}}$ $=(2^2)^color(purple)sqrt7$

$=4^color(purple)sqrt7 ~~ 39.16525...$

That's as simplified as it gets, unfortunately.

Answer 2 · 2018-03-10T20:15:32

$4^7= 16384$

$2^sqrt7*2^sqrt7$
$2*2=4$
$1^sqrt7*1^sqrt7= 1^7$
$4*1^7= 4^7$
$4*4*4*4*4*4*4= 4^7= 16384$

How do you simplify 2^sqrt7*2^sqrt72√7⋅2√72^sqrt7*2^sqrt7?