# How do you simplify 8/(m^2) * (m^2/(2c))^2?

Jul 25, 2015

Cancel the terms common to the numerator and to the denominator.

#### Explanation:

Your initial expression looks like this

$\frac{8}{m} ^ 2 \cdot {\left({m}^{2} / \left(2 c\right)\right)}^{2}$

Notice that you have ${m}^{2}$ as the denominator of the first fraction and ${\left({m}^{2}\right)}^{2}$ as the numerator of the second fraction. This means that you can write

$\frac{8}{m} ^ 2 \cdot {\left({m}^{2}\right)}^{2} / \left({\left(2 c\right)}^{2}\right) = \frac{8}{m} ^ 2 \cdot \frac{{m}^{2} \cdot {m}^{2}}{{2}^{2} \cdot {c}^{2}} = \frac{\cancel{4} \cdot 2}{\cancel{{m}^{2}}} \cdot \frac{\cancel{{m}^{2}} \cdot {m}^{2}}{\cancel{4} \cdot {c}^{2}}$

Your initial expression will thus be equivalent to

$\frac{8}{m} ^ 2 \cdot {\left({m}^{2} / \left(2 c\right)\right)}^{2} = \textcolor{g r e e n}{\frac{2 \cdot {m}^{2}}{c}}$