# How do you multiply (8w^2)/9*3/(2w^4)?

Aug 21, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

$\left(\frac{8 \cdot 3}{9 \cdot 2}\right) \left({w}^{2} / {w}^{4}\right) \implies \left(\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} 4 \cdot \textcolor{b l u e}{\cancel{\textcolor{b l a c k}{3}}}}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{9}}} 3 \cdot \textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right) \left({w}^{2} / {w}^{4}\right) \implies$

$\frac{4}{3} \left({w}^{2} / {w}^{4}\right)$

We can now use this rule for exponents to simplify the $w$ terms:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

$\frac{4}{4} \left({w}^{\textcolor{red}{2}} / {w}^{\textcolor{b l u e}{4}}\right) \implies \frac{4}{3} \cdot \frac{1}{w} ^ \left(\textcolor{b l u e}{4} - \textcolor{red}{2}\right) \implies \frac{4}{3} \cdot \frac{1}{w} ^ 2 \implies$

$\frac{4}{3 {w}^{2}}$