# How do you simplify (k^4m^3p^2)/(k^2m^2)?

May 19, 2017

See a solution process below:

#### Explanation:

First, rewrite this expression as:

$\left({k}^{4} / {k}^{2}\right) \left({m}^{3} / {m}^{2}\right) {p}^{2}$

Next, use this rule of exponents to simplify the $k$ and $m$ terms:

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

$\left({k}^{\textcolor{red}{4}} / {k}^{\textcolor{b l u e}{2}}\right) \left({m}^{\textcolor{red}{3}} / {m}^{\textcolor{b l u e}{2}}\right) {p}^{2} \implies {k}^{\textcolor{red}{4} - \textcolor{b l u e}{2}} {m}^{\textcolor{red}{3} - \textcolor{b l u e}{2}} {p}^{2} \implies {k}^{2} {m}^{1} {p}^{2}$

Now, use this rule of exponents to further simplify the $m$ term:

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

${k}^{2} {m}^{\textcolor{red}{1}} {p}^{2} = {k}^{2} m {p}^{2}$