# How do you simplify (4m^4n^3p^3)/(3m^2n^2p^4) and write it using only positive exponents?

Mar 6, 2017

See the entire simplification process below:

#### Explanation:

First, rewrite as:

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

Now, use these rules of exponents to begin the simplification:

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

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

$\frac{4 {m}^{2} {n}^{1}}{3 {p}^{1}}$

We can use this rule of exponents to complete the simplification:

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

$\frac{4 {m}^{2} {n}^{\textcolor{red}{1}}}{3 {p}^{\textcolor{red}{1}}} = \frac{4 {m}^{2} n}{3 p}$