# How do you simplify ((1/2)x^4)^3?

May 26, 2016

$\frac{{x}^{12}}{8}$

#### Explanation:

This is the same as ${\left({x}^{4}\right)}^{3} \times {\left(\frac{1}{2}\right)}^{3}$

$\left({x}^{4 \times 3}\right) \times \frac{1}{{2}^{3}}$

${x}^{12} \times \frac{1}{8} \text{ "->" } \frac{{x}^{12}}{8}$

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Further explanation:

Consider:$\text{ } {\left({x}^{4}\right)}^{3}$ This is another way of writing ${x}^{4} \times {x}^{4} \times {x}^{4}$

Think for a moment about $a \times a \to {a}^{1} \times {a}^{1} = {a}^{1 + 1} = {a}^{2 \times 1} = {a}^{2}$

so ${x}^{4} \times {x}^{4} \times {x}^{4} = {x}^{4 + 4 + 4} = {x}^{3 \times 4}$

So ${\left({x}^{4}\right)}^{3} = {x}^{4 \times 3} = {x}^{12}$
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