# How do you simplify (3x^3)^2*(2x)^3 and write it using only positive exponents?

Apr 19, 2017

$72 {x}^{9}$

#### Explanation:

using the $\textcolor{b l u e}{\text{laws of exponents}}$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{{\left({a}^{m} {b}^{n}\right)}^{p} = {a}^{m p} {b}^{n p} \text{ and } {a}^{m} \times {a}^{n} = {a}^{m + n}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\Rightarrow {\left(3 {x}^{3}\right)}^{2} \times {\left(2 x\right)}^{3}$

$= {3}^{\left(1 \times 2\right)} \times {x}^{\left(3 \times 2\right)} \times {2}^{\left(1 \times 3\right)} \times {x}^{\left(1 \times 3\right)}$

$= {3}^{2} \times {x}^{6} \times {2}^{3} \times {x}^{3}$

$= 9 \times 8 \times {x}^{\left(6 + 3\right)}$

$= 72 {x}^{9}$