# How do you simplify -(3a^6 b^4)^3?

Jun 19, 2018

See a solution process below:

#### Explanation:

First, use this rule for exponents to rewrite the $3$ term:

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

$- {\left(3 {a}^{6} {b}^{4}\right)}^{3} \implies - {\left({3}^{\textcolor{red}{1}} {a}^{6} {b}^{4}\right)}^{3}$

Next, use this rule to eliminate the outer exponent:

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

$- {\left({3}^{\textcolor{red}{1}} {a}^{\textcolor{red}{6}} {b}^{\textcolor{red}{4}}\right)}^{\textcolor{b l u e}{3}} \implies - {3}^{\textcolor{red}{1} \times \textcolor{b l u e}{3}} {a}^{\textcolor{red}{6} \times \textcolor{b l u e}{3}} {b}^{\textcolor{red}{4} \times \textcolor{b l u e}{3}} \implies - {3}^{3} {a}^{18} {b}^{12} \implies - 27 {a}^{18} {b}^{12}$