Divide $ \dfrac{10x^4}{3xy^2} $ by $ \dfrac{6x^2y}{xy^4} $ to get $ \dfrac{ 10x^5y^4 }{ 18x^3y^3 } $.

Step 1: To divide rational expressions, multiply the first fraction by the reciprocal of the second fraction.

Step 2: Multiply numerators and denominators.

Step 3: Simplify numerator and denominator.

$$ \begin{aligned} \frac{ \frac{10x^4}{3xy^2} }{ \frac{\color{blue}{6x^2y}}{\color{blue}{xy^4}} } & \xlongequal{\text{Step 1}} \frac{10x^4}{3xy^2} \cdot \frac{\color{blue}{xy^4}}{\color{blue}{6x^2y}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 10x^4 \cdot xy^4 }{ 3xy^2 \cdot 6x^2y } \xlongequal{\text{Step 3}} \frac{ 10x^5y^4 }{ 18x^3y^3 } \end{aligned} $$