# How do you simplify (2m^-4)/(2m^-4)^3 and write it using only positive exponents?

Feb 28, 2017

See the entire solution process below:

#### Explanation:

First, we can simplify the denominator using these rules for exponents:

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

$\frac{2 {m}^{-} 4}{2 {m}^{-} 4} ^ 3 = \frac{2 {m}^{-} 4}{{2}^{\textcolor{red}{1}} {m}^{\textcolor{red}{- 4}}} ^ \textcolor{b l u e}{3} = \frac{2 {m}^{-} 4}{{2}^{\textcolor{red}{1} \times \textcolor{b l u e}{3}} {m}^{\textcolor{red}{- 4} \times \textcolor{b l u e}{3}}} = \frac{2 {m}^{-} 4}{{2}^{3} {m}^{-} 12}$

We can now use these rules for exponents to complete the simplification:

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

$\frac{2 {m}^{-} 4}{{2}^{3} {m}^{-} 12} = \frac{{2}^{\textcolor{red}{1}} {m}^{\textcolor{red}{- 4}}}{{2}^{\textcolor{b l u e}{3}} {m}^{\textcolor{b l u e}{- 12}}} = \frac{{m}^{\textcolor{red}{- 4} - \textcolor{b l u e}{- 12}}}{{2}^{\textcolor{b l u e}{3} - \textcolor{red}{1}}} = \frac{{m}^{\textcolor{red}{- 4} + \textcolor{b l u e}{12}}}{2} ^ 2 = {m}^{8} / 4$