# How do you simplify (2m)^-3 and write it using only positive exponents?

Apr 23, 2017

See the entire solution process below:

#### Explanation:

First, use this rule of exponents to eliminate the negative exponent:

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

${\left(2 m\right)}^{\textcolor{red}{- 3}} = \frac{1}{2 m} ^ \textcolor{red}{- - 3} = \frac{1}{2 m} ^ 3$

Next, use these two rules of exponents to complete the simplification:

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

$\frac{1}{2 m} ^ 3 \implies \frac{1}{{2}^{\textcolor{red}{1}} {m}^{\textcolor{red}{1}}} ^ \textcolor{b l u e}{3} \implies \frac{1}{{2}^{\textcolor{red}{1} \times \textcolor{b l u e}{3}} {m}^{\textcolor{red}{1} \times \textcolor{b l u e}{3}}} \implies \frac{1}{{2}^{3} {m}^{3}} \implies \frac{1}{8 {m}^{3}}$