Divide $ \dfrac{16x^2y}{81xy^2} $ by $ \dfrac{24x^2y}{54x^3y^3} $ to get $ \dfrac{ 864x^5y^4 }{ 1944x^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.

$$ \begin{aligned} \frac{ \frac{16x^2y}{81xy^2} }{ \frac{\color{blue}{24x^2y}}{\color{blue}{54x^3y^3}} } & \xlongequal{\text{Step 1}} \frac{16x^2y}{81xy^2} \cdot \frac{\color{blue}{54x^3y^3}}{\color{blue}{24x^2y}} = \\[1ex] & \xlongequal{\text{Step 2}} \frac{ 16x^2y \cdot 54x^3y^3 }{ 81xy^2 \cdot 24x^2y } \xlongequal{\text{Step 3}} \frac{ 864x^5y^4 }{ 1944x^3y^3 } \end{aligned} $$