# How do you simplify (2a^-2)/(2a)^-3?

Mar 12, 2017

See the entire solution process below:

#### Explanation:

First, use these rules for exponents to simplify the denominator:

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

$\frac{2 {a}^{-} 2}{{\left(2 a\right)}^{-} 3} = \frac{2 {a}^{-} 2}{{\left({2}^{\textcolor{red}{1}} {a}^{\textcolor{red}{1}}\right)}^{\textcolor{b l u e}{- 3}}} = \frac{2 {a}^{-} 2}{\left({2}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 3}} {a}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 3}}\right)} = \frac{2 {a}^{-} 2}{{2}^{-} 3 {a}^{-} 3}$

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

$a = {a}^{\textcolor{red}{1}}$ and ${a}^{\textcolor{red}{1}} = a$ and ${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} - \textcolor{b l u e}{b}}$

(2a^-2)/(2^-3a^-3) = (2^color(red)(1)a^color(red)(-2))/(2^color(blue)(-3)a^color(blue)(-3)) = 2^(color(red)(1)-color(blue)(-3))a^(color(red)(-2)-color(blue)(-3)) = 2^(color(red)(1)+color(blue)(3))a^(color(red)(-2)+color(blue)(3) =

${2}^{4} {a}^{1} = 16 a$