# How do you simplify (144)/(4xy)div (54y^3)/(3x^3y)?

Aug 26, 2016

Dividing by a fraction is the same as multiplying with the inverse.

#### Explanation:

So we invert the second fraction (=put it upside down):
$= \frac{144}{4 x y} \times \frac{3 {x}^{3} y}{54 {y}^{3}} = \frac{144 \cdot 3 {x}^{3} y}{4 \cdot 54 x y \cdot {y}^{3}} = \frac{432 {x}^{3} y}{216 x {y}^{4}}$

Then we factorize as far as necessary, and cancel:
$= \frac{2 \cdot \cancel{216} \cdot \cancel{x} \cdot x \cdot x \cdot \cancel{y}}{\cancel{216} \cdot \cancel{x} \cdot \cancel{y} \cdot y \cdot y \cdot y} = \frac{2 {x}^{2}}{y} ^ 3$