# How do you multiply (3x ^ { 2} \cdot x ^ { 3} ) ^ { 2}?

##### 1 Answer
Jun 2, 2017

See a solution process below:

#### Explanation:

First, multiply the $x$ terms within the parenthesis using this rule for exponents:

${x}^{\textcolor{red}{a}} \times {x}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} + \textcolor{b l u e}{b}}$

${\left(3 {x}^{\textcolor{red}{2}} \cdot {x}^{\textcolor{b l u e}{3}}\right)}^{2} \implies {\left(3 {x}^{\textcolor{red}{2} + \textcolor{b l u e}{3}}\right)}^{2} \implies {\left(3 {x}^{5}\right)}^{2}$

We can now use these two rules of exponents to complete the multiplication:

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

${\left(3 {x}^{5}\right)}^{2} \implies {\left({3}^{\textcolor{red}{1}} {x}^{\textcolor{red}{5}}\right)}^{\textcolor{b l u e}{2}} \implies {3}^{\textcolor{red}{1} \times \textcolor{b l u e}{2}} {x}^{\textcolor{red}{5} \times \textcolor{b l u e}{2}} \implies {3}^{2} {x}^{10} \implies$

$9 {x}^{10}$