How do you simplify (-3m^4n)/(12m^6n^4)?

Aug 2, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

$\left(- \frac{3}{12}\right) \left({m}^{4} / {m}^{6}\right) \left(\frac{n}{n} ^ 4\right) \implies - \frac{1}{4} \left({m}^{4} / {m}^{6}\right) \left(\frac{n}{n} ^ 4\right)$

Next, use this rule of exponents to rewrite the numerator for the $n$ term:

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

$- \frac{1}{4} \left({m}^{4} / {m}^{6}\right) \left({n}^{\textcolor{red}{1}} / {n}^{4}\right)$

Now, use this rule of exponents to complete the simplification for the $m$ and $n$ terms:

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

$- \frac{1}{4} \left({m}^{\textcolor{red}{4}} / {m}^{\textcolor{b l u e}{6}}\right) \left({n}^{\textcolor{red}{1}} / {n}^{\textcolor{b l u e}{4}}\right) \implies$

$- \frac{1}{4} \left(\frac{1}{m} ^ \left(\textcolor{b l u e}{6} - \textcolor{red}{4}\right)\right) \left(\frac{1}{n} ^ \left(\textcolor{b l u e}{4} - \textcolor{red}{1}\right)\right) \implies$

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

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