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

May 8, 2017

See a solution process below:

Explanation:

First, simplify the term within the outer parenthesis by using this rule of exponents:

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

${\left({\left({a}^{\textcolor{red}{- 2}}\right)}^{\textcolor{b l u e}{2}}\right)}^{-} 3 = {\left({a}^{\textcolor{red}{- 2} \times \textcolor{b l u e}{2}}\right)}^{-} 3 \implies {\left({a}^{-} 4\right)}^{-} 3$

Use this same rule to simplify the remaining expression:

${\left({a}^{\textcolor{red}{- 4}}\right)}^{\textcolor{b l u e}{- 3}} = {a}^{\textcolor{red}{- 4} \times \textcolor{b l u e}{- 3}} = {a}^{12}$