# How do you simplify (m^4n^-2)(m^2n^3)?

Mar 14, 2017

See the entire solution process below:

#### Explanation:

First, rewrite this expression as:

$\left({m}^{4} \cdot {m}^{2}\right) \left({n}^{-} 2 \cdot {n}^{3}\right)$

Next, use this rule of exponents to combine the terms:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

$\left({m}^{\textcolor{red}{4}} \cdot {m}^{\textcolor{b l u e}{2}}\right) \left({n}^{\textcolor{red}{- 2}} \cdot {n}^{\textcolor{b l u e}{3}}\right) = {m}^{\textcolor{red}{4} + \textcolor{b l u e}{2}} {x}^{\textcolor{red}{- 2} + \textcolor{b l u e}{3}} = {m}^{6} {n}^{1}$

Now, use this rule of exponents to complete the simplification:

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

${m}^{6} {n}^{\textcolor{red}{1}} = {m}^{6} n$