# How do you multiply (27r^5)/(7s)*(28rs^3)/(9r^3s^2)?

Mar 3, 2018

The simplified answer is $12 {r}^{3}$.

#### Explanation:

First, simplify given expression:

$\textcolor{w h i t e}{=} \frac{27 {r}^{5}}{7 s} \cdot \frac{28 r {s}^{3}}{9 {r}^{3} {s}^{2}}$

$= \frac{27 {r}^{5}}{7 s} \cdot \frac{28 \textcolor{red}{\cancel{\textcolor{b l a c k}{r}}} {s}^{3}}{9 {r}^{\stackrel{2}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}} {s}^{2}}$

=(27r^5)/(7s)*(28s^color(red)cancel(color(black)3))/(9r^2color(red)cancel(color(black)(s^2))

$= \frac{27 {r}^{5}}{7 s} \cdot \frac{28 s}{9 {r}^{2}}$

Next, multiply the numerators and denominators:

$\textcolor{w h i t e}{=} \frac{27 {r}^{5}}{7 s} \cdot \frac{28 s}{9 {r}^{2}}$

$= \frac{27 {r}^{5} \cdot 28 s}{7 s \cdot 9 {r}^{2}}$

$= \frac{756 {r}^{5} s}{63 {r}^{2} s}$

$= \frac{\stackrel{12}{\textcolor{red}{\cancel{\textcolor{b l a c k}{756}}}} {r}^{5} s}{\textcolor{red}{\cancel{\textcolor{b l a c k}{63}}} {r}^{2} s}$

$= \frac{12 {r}^{\stackrel{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}}} s}{\textcolor{red}{\cancel{\textcolor{b l a c k}{{r}^{2}}}} s}$

$= \frac{12 {r}^{3} \textcolor{red}{\cancel{\textcolor{b l a c k}{s}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{s}}}}$

$= 12 {r}^{3}$

This is as simplified as it gets.