How do you simplify ${(\frac{2 ∙ 2^{3}}{2})}^{2}$ $((2•2^3) / 2) ^2$ ?

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Answer 1 · 2016-07-11T19:07:40

Assuming you mean ${(\frac{2 \times 2^{3}}{2})}^{2}$ $((2xx2^3)/2)^2$

64

I have deliberately done it this way to demonstrate some actions

$2 \times 2^{3} = 2^{3 + 1} = 2^{4}$ $2xx2^3 = 2^(3+1) =2^4$ giving

${(\frac{2^{4}}{2})}^{2}$ $((2^4)/2)^2$

But $\frac{2^{4}}{2}$ $2^4/2$ is the same as $2^(4-1)=(cancel(2)xx2xx2xx2)/(cancel(2)) =2^3$ giving:

$(2^3)^2$

But this is the same as $2^3xx2^3" " =" " 2^(3+3)" "=" "2^(3xx2) = 64$
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$color(blue)("Using shortcuts")$

$((cancel(2)xx2^3)/(cancel(2)))^2 = 2^6=64$

How do you simplify ((2•2^3) / 2) ^2(2∙232)2((2•2^3) / 2) ^2?