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

Oct 29, 2015

${x}^{8} / 256$

#### Explanation:

You can multiply exponents into the brackets as long as it is multiplying and dividing. DO NOT DO THIS FOR ADDITION AND SUBTRACTION!!

Examples:
In multiplication we, would distribute the exponent by multiplying it. For example, if I had ${\left(x \times 2\right)}^{2}$, I could put this as ${\left({x}^{1 \times \textcolor{red}{2}} \times {2}^{1 \times \textcolor{red}{2}}\right)}^{\cancel{\textcolor{red}{2}}} \Rightarrow \left({x}^{2} \times 4\right)$.

Another example: If I had ${\left({x}^{3} \div {y}^{9}\right)}^{5}$, I could distribute the exponent like this:
${\left({x}^{3 \cdot \textcolor{red}{5}} \times {y}^{4 \times \textcolor{red}{5}}\right)}^{\cancel{\textcolor{red}{5}}} \Rightarrow \left({x}^{15} \times {y}^{20}\right)$

For this question:
${\left({x}^{2} / 4\right)}^{4}$ can be written as ${\left({x}^{2} \div 4\right)}^{4}$

We distribute the exponent:

$\left({x}^{2 \times 4} \div {4}^{1 \times 4}\right) \Rightarrow \left({x}^{8} \div {4}^{4}\right)$

Put it back in numerator/denominator form:

${x}^{8} / {4}^{4}$

Expand ${4}^{4}$

$= {x}^{8} / 256$

Oct 29, 2015

${\left(\frac{{x}^{2}}{4}\right)}^{4} = \frac{{x}^{8}}{256}$

#### Explanation:

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

Apply exponent rule ${\left({a}^{m}\right)}^{n} = {a}^{m \cdot n}$

$\frac{{x}^{2 \cdot 4}}{{4}^{1 \cdot 4}} =$

$\frac{{x}^{8}}{256}$