1. **State the problem:** Simplify the expression $\frac{(x^3)(x + 5)}{x - 9} \cdot \frac{(x - 9)(x + 8)}{3x^3}$. 2. **Write the formula and rules:** When multiplying fractions, multiply numerators together and denominators together: $$\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}$$ Also, factor and cancel common factors to simplify. 3. **Apply multiplication:** $$\frac{(x^3)(x + 5)}{x - 9} \cdot \frac{(x - 9)(x + 8)}{3x^3} = \frac{(x^3)(x + 5)(x - 9)(x + 8)}{(x - 9)(3x^3)}$$ 4. **Cancel common factors:** The factor $x - 9$ appears in numerator and denominator, and $x^3$ also appears in numerator and denominator: $$\frac{\cancel{(x - 9)} \cancel{x^3} (x + 5)(x + 8)}{\cancel{(x - 9)} 3 \cancel{x^3}} = \frac{(x + 5)(x + 8)}{3}$$ 5. **Multiply remaining factors in numerator:** $$(x + 5)(x + 8) = x^2 + 8x + 5x + 40 = x^2 + 13x + 40$$ 6. **Final simplified expression:** $$\frac{x^2 + 13x + 40}{3}$$ **Answer:** $$\boxed{\frac{x^2 + 13x + 40}{3}}$$