# How do you simplify (c^3)^2(-3c^5)^2?

Jan 7, 2017

See full process explanation below

#### Explanation:

First, we simplify the terms within parenthesis using this rule for exponents:

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

${\left({c}^{3}\right)}^{2} {\left(- 3 {c}^{5}\right)}^{2} \to {c}^{3 \times 2} \times - {3}^{2} {c}^{5 \times 2} \to {c}^{6} \times - 27 {c}^{10}$

We can then use this other rule of exponents to finalize the simplification:

x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b)

${c}^{6} \times - 27 {c}^{10} \to - 27 {c}^{6 + 10} \to - 27 {c}^{16}$