# How do you simplify (5/(4x^2)) / (8/x^3)?

Sep 3, 2016

$\frac{\frac{5}{4 {x}^{2}}}{\frac{8}{{x}^{3}}} = \frac{5 x}{32}$

#### Explanation:

Multiply the "lowest common multiple" to both the numerator and the denominator.

A nice common multiple of $4 {x}^{2}$ and ${x}^{3}$ is $4 {x}^{3}$.

So trying to multiply out

$\frac{\frac{5}{4 {x}^{2}} \cdot \left(4 {x}^{3}\right)}{\frac{8}{{x}^{3}} \cdot \left(4 {x}^{3}\right)} = \frac{5 x}{32}$

Sep 3, 2016

$\frac{5 x}{32}$

#### Explanation:

When you have a fraction over a fraction, you can make use of the following as the first step in simplifying.

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{b l u e}{c}}{\textcolor{red}{d}}} = \frac{\textcolor{red}{a \times d}}{\textcolor{b l u e}{b \times c}}$

$\frac{\frac{5}{4 {x}^{2}}}{\frac{8}{x} ^ 3} = \frac{5 \times {x}^{3}}{4 {x}^{2} \times 8} \text{ "larr" simplify}$

=$\frac{5 x}{32}$