1. **Problem:** Multiply the rational expressions $\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}$ and simplify. 2. **Step 1: Factor all numerators and denominators completely.** - Numerator: $5y^3 \times (-4) = -20y^3$ - Denominator: $32x \times 15x^2 y^3 = 480x^3 y^3$ 3. **Step 2: Divide out common factors.** - $y^3$ cancels out from numerator and denominator. - $20$ and $480$ have a common factor of $20$, so $\frac{-20}{480} = \frac{-1}{24}$. - $x^3$ remains in denominator. 4. **Step 3: Multiply the numerator and denominator completely.** - Simplified expression: $\frac{-1}{24x^3}$ **Final answer:** $\boxed{\frac{-1}{24x^3}}$