# How do you simplify \frac { - 3m ^ { 5} n ^ { 4} } { 2m ^ { - 6} n ^ { 0} }?

Jan 20, 2018

See a solution process below:

#### Explanation:

First, rewrite the expression as:

$\left(- \frac{3}{2}\right) \left({m}^{5} / {m}^{-} 6\right) \left({n}^{4} / {n}^{0}\right) \implies - \frac{3}{2} \left({m}^{5} / {m}^{-} 6\right) \left({n}^{4} / {n}^{0}\right)$

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

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

$- \frac{3}{2} \left({m}^{\textcolor{red}{5}} / {m}^{\textcolor{b l u e}{- 6}}\right) \left({n}^{4} / {n}^{0}\right) \implies$

$- \frac{3}{2} \left({m}^{\textcolor{red}{5} - \textcolor{b l u e}{- 6}}\right) \left({n}^{4} / {n}^{0}\right) \implies$

$- \frac{3}{2} \left({m}^{\textcolor{red}{5} + \textcolor{b l u e}{6}}\right) \left({n}^{4} / {n}^{0}\right) \implies$

$- \frac{3}{2} \left({m}^{11}\right) \left({n}^{4} / {n}^{0}\right) \implies$

$\frac{- 3 {m}^{11}}{2} \left({n}^{4} / {n}^{0}\right)$

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

${a}^{\textcolor{red}{0}} = 1$

$\frac{- 3 {m}^{11}}{2} \left({n}^{4} / {n}^{\textcolor{red}{0}}\right) \implies$

$\frac{- 3 {m}^{11}}{2} \left({n}^{4} / 1\right) \implies$

$\frac{- 3 {m}^{11}}{2} \left({n}^{4}\right) \implies$

$\frac{- 3 {m}^{11} {n}^{4}}{2}$