# How do you simplify ((5n^4)/(p^3))/((6n)/(5p))?

Jan 16, 2017

See the entire simplification process below:

#### Explanation:

First, simplify the division by using the rule for dividing fractions:

$\frac{\frac{\textcolor{red}{a}}{\textcolor{b l u e}{b}}}{\frac{\textcolor{g r e e n}{c}}{\textcolor{p u r p \le}{d}}} = \frac{\textcolor{red}{a} \times \textcolor{p u r p \le}{d}}{\textcolor{b l u e}{b} \times \textcolor{g r e e n}{c}}$

$\frac{\frac{\textcolor{red}{5 {n}^{4}}}{\textcolor{b l u e}{{p}^{3}}}}{\frac{\textcolor{g r e e n}{6 n}}{\textcolor{p u r p \le}{5 p}}} = \frac{\textcolor{red}{5 {n}^{4}} \times \textcolor{p u r p \le}{5 p}}{\textcolor{b l u e}{{p}^{3}} \times \textcolor{g r e e n}{6 n}} = \frac{25 {n}^{4} p}{6 n {p}^{3}}$

We can now use these rules for exponents to further simplify this expression:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

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

$\frac{25 {n}^{\textcolor{red}{4}} {p}^{\textcolor{red}{1}}}{6 {n}^{\textcolor{b l u e}{1}} {p}^{\textcolor{b l u e}{3}}}$

$\frac{25 {n}^{\textcolor{red}{4} - \textcolor{b l u e}{1}}}{6 {p}^{\textcolor{b l u e}{3} - \textcolor{red}{1}}}$

$\frac{25 {n}^{3}}{6 {p}^{2}}$