How do you simplify (2x)/(y²) * (3y³)/(4x²)?

Jul 25, 2015

Cancel equal terms from the numerator and the denominator.

Explanation:

Your starting expression looks like this

$\frac{2 x}{{y}^{2}} \cdot \frac{3 {y}^{3}}{4 {x}^{2}}$

You know that you can write $3 {y}^{3}$ and $4 {x}^{2}$ as

$3 {y}^{3} = 3 {y}^{2} \cdot y$

$4 {x}^{2} = {\left(2 x\right)}^{2} = 2 x \cdot 2 x$

$\frac{\cancel{2 x}}{\cancel{{y}^{2}}} \cdot \frac{3 \cdot \cancel{{y}^{2}} \cdot y}{\cancel{2 x} \cdot 2 x} = \textcolor{g r e e n}{\frac{3 y}{2 x}}$