# How do you find the quotient of (3r^4)/k^2div(18r^3)/k?

Feb 10, 2017

See the entire solution process below:

#### Explanation:

First, we can rewrite this expression as:

$\frac{\frac{3 {r}^{4}}{k} ^ 2}{\frac{18 {r}^{3}}{k}}$

We can now use this rule for dividing fractions:

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

$\frac{\frac{\textcolor{red}{3 {r}^{4}}}{\textcolor{b l u e}{{k}^{2}}}}{\frac{\textcolor{g r e e n}{18 {r}^{3}}}{\textcolor{p u r p \le}{k}}} = \frac{\textcolor{red}{3 {r}^{4}} \times \textcolor{p u r p \le}{k}}{\textcolor{b l u e}{{k}^{2}} \times \textcolor{g r e e n}{18 {r}^{3}}} = \frac{3 k {r}^{4}}{18 {k}^{2} {r}^{3}} = \frac{k {r}^{4}}{6 {k}^{2} {r}^{3}}$

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

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

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

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

$\frac{k {r}^{4}}{6 {k}^{2} {r}^{3}} = \frac{{k}^{1} {r}^{4}}{6 {k}^{2} {r}^{3}} = {r}^{4 - 3} / \left(6 {k}^{2 - 1}\right) = {r}^{1} / \left(6 {k}^{1}\right) = \frac{r}{6 k}$

Feb 10, 2017

$\frac{r}{6 k}$

#### Explanation:

To divide by a decimal. multiply by its reciprocal.

$\frac{3 {r}^{4}}{{k}^{2}} \textcolor{b l u e}{\div \frac{18 {r}^{3}}{k}}$

$= \frac{3 {r}^{4}}{{k}^{2}} \textcolor{b l u e}{\times \frac{k}{18 {r}^{3}}}$

$= \frac{\cancel{3} k {r}^{4}}{{\cancel{18}}_{6} {k}^{2} {r}^{3}} \text{ } \leftarrow$ subtract indices of like bases

$= \frac{r}{6 k}$