# How do you multiply and simplify to the lowest terms \frac{x^3}{2y^3} \cdot \frac{2y^2}{x}?

Nov 3, 2014

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

by multiplying the numerators together and the numerators together,

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

by dividing the numerator and the denominator by $2$,

$= \frac{{x}^{3} {y}^{2}}{x {y}^{3}}$

by dividing the numerator and the denominator by $x$,

$= \frac{{x}^{2} {y}^{2}}{{y}^{3}}$

by dividing the numerator and the denominator by ${y}^{2}$,

$= \frac{{x}^{2}}{y}$

I hope that this was helpful.