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

May 10, 2018

$27 {x}^{3} {y}^{3}$

#### Explanation:

$\frac{1}{3 y} ^ \left(- 2\right) = {\left(3 y\right)}^{2}$

$\frac{3 {x}^{3} y}{3 y} ^ \left(- 2\right) = 3 {x}^{3} y \times {\left(3 y\right)}^{2}$

$= 3 {x}^{3} y \times 9 {y}^{2} = 27 {x}^{3} {y}^{3}$

May 10, 2018

$\frac{3 {x}^{3} y}{3 y} ^ \left(- 2\right)$ = $= 27 {x}^{3} {y}^{3}$ = ${\left(3 x y\right)}^{3}$

#### Explanation:

You want to simplify $\frac{3 {x}^{3} y}{3 y} ^ \left(- 2\right)$

We must remember that $\frac{1}{x} ^ - n = {x}^{n}$
Therefore $\frac{1}{3 y} ^ \left(- 2\right) = {\left(3 y\right)}^{2}$

We, therefore, can write:
$\frac{3 {x}^{3} y}{3 y} ^ \left(- 2\right)$
$= \left(3 {x}^{3} y\right) {\left(3 y\right)}^{2}$
$= 3 {x}^{3} y \cdot {3}^{2} {y}^{2}$
$= 27 {x}^{3} {y}^{3}$

As $27 = {3}^{3}$ it's perhaps a little more elegant if we write this
${\left(3 x y\right)}^{3}$