# How do you simplify ((2x^-1) / (3y^2)^2) times (3x^2)/(5y)?

Apr 16, 2016

$\frac{6 x}{45 {y}^{5}}$

Every step shown to aid understanding. As you become practised you will be able to skip steps.

#### Explanation:

Splitting the given expression down into its component parts

color(blue)("Consider "2x^(-1)

This is another way of writing: $\textcolor{g r e e n}{\frac{2}{x}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider } \frac{1}{{\left(3 {y}^{2}\right)}^{2}}}$

This is another way of writing: $\textcolor{g r e e n}{\frac{1}{9 {y}^{4}}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Putting it all together}}$

$\frac{2}{x} \times \frac{1}{9 {y}^{4}} \times \frac{3 {x}^{2}}{5 y}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Simplifying}}$

$\frac{2 \times 1 \times 3 {x}^{2}}{x \times 9 {y}^{4} \times 5 y}$

$\frac{6 {x}^{2}}{45 x {y}^{5}}$

Separate out the $x ' s$

${x}^{2} / x \times \frac{6}{45 {y}^{5}}$

$\frac{x \times x}{x} \times \frac{6}{45 {y}^{5}}$

$\frac{x}{x} \times \frac{x}{1} \times \frac{6}{45 {y}^{5}}$

But $\frac{x}{x} = 1$

$1 \times \frac{x}{1} \times \frac{6}{45 {y}^{5}}$

$\frac{6 x}{45 {y}^{5}}$