1. Problem: Multiply the rational expressions \(\frac{5y^3}{32x} \times \frac{-4}{15x^2 y^3}\). 2. Formula: To multiply rational expressions, multiply the numerators and denominators: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. Factor and simplify: - Numerator: \(5y^3 \times -4 = -20y^3\) - Denominator: \(32x \times 15x^2 y^3 = 480x^3 y^3\) 4. Divide out common factors: - \(y^3\) cancels out numerator and denominator. - \(20\) and \(480\) simplify to \(1\) and \(24\) respectively. 5. Result: $$\frac{-1}{24x^3}$$ Final answer: \(-\frac{1}{24x^3}\)