Answer
$= \frac{4x^{3}}{5y^{2}}$
Work Step by Step
Recall, dividing by a fraction is the same as multiplying by the reciprocal of that fraction. Thus, we obtain:
$(\frac{6xy}{9y^{2}}) \div (\frac{15y}{18x^{2}})$
$= (\frac{6xy}{9y^{2}}) \times (\frac{18x^{2}}{15y})$
$= \frac{6xy(18x^{2})}{9y^{2}(15y)}$
$= \frac{108x^{3}y}{135y^{3}}$
$= \frac{4x^{3}}{5y^{2}}$
