# How do you simplify and write (-3m)^-4 with positive exponents?

Jun 15, 2018

See a solution process below:

#### Explanation:

First, use this rule of exponents to rewrite the terms within the parenthesis:

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

${\left(- {3}^{\textcolor{red}{1}} {m}^{\textcolor{red}{1}}\right)}^{-} 4$

Next, use this rule of exponents to eliminate the parenthesis:

${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

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

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

${x}^{\textcolor{red}{a}} = \frac{1}{x} ^ \textcolor{red}{- a}$

$- {3}^{\textcolor{red}{- 4}} {m}^{\textcolor{red}{- 4}} \implies \frac{1}{-} {3}^{\textcolor{red}{- - 4}} \cdot \frac{1}{m} ^ \textcolor{red}{- - 4} \implies \frac{1}{-} {3}^{4} \cdot \frac{1}{m} ^ 4 \implies \frac{1}{81} \cdot \frac{1}{m} ^ 4 \implies \frac{1}{81 {m}^{4}}$