# How do you simplify (\frac{2}{a^{2}})^{2}?

Mar 28, 2018

$\frac{4}{a} ^ 4$

#### Explanation:

= ${\left(\frac{2}{a} ^ 2\right)}^{2}$

= $\frac{2}{a} ^ 2 \cdot \frac{2}{a} ^ 2$

= $\frac{4}{a} ^ 4$

Mar 28, 2018

See a solution process below:

#### Explanation:

First, use this rule of exponents to rewrite the numerator:

$c = {c}^{\textcolor{red}{1}}$

${\left(\frac{2}{a} ^ 2\right)}^{2} = {\left({2}^{\textcolor{red}{1}} / {a}^{2}\right)}^{2}$

Now, use this rule of exponents to complete the simplification:

${\left({x}^{\textcolor{red}{j}}\right)}^{\textcolor{b l u e}{k}} = {x}^{\textcolor{red}{j} \times \textcolor{b l u e}{k}}$

${\left({2}^{\textcolor{red}{1}} / {a}^{\textcolor{red}{2}}\right)}^{\textcolor{b l u e}{2}} \implies {2}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} / {a}^{\textcolor{red}{2} \times \textcolor{b l u e}{2}} \implies {2}^{2} / {a}^{4} = \frac{4}{a} ^ 4$