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

Jul 11, 2016

Assuming you mean ${\left(\frac{2 \times {2}^{3}}{2}\right)}^{2}$

64

#### Explanation:

I have deliberately done it this way to demonstrate some actions

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

${\left(\frac{{2}^{4}}{2}\right)}^{2}$

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

${\left({2}^{3}\right)}^{2}$

But this is the same as ${2}^{3} \times {2}^{3} \text{ " =" " 2^(3+3)" "=" } {2}^{3 \times 2} = 64$
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$\textcolor{b l u e}{\text{Using shortcuts}}$

${\left(\frac{\cancel{2} \times {2}^{3}}{\cancel{2}}\right)}^{2} = {2}^{6} = 64$