1. **State the problem:** Simplify the expression $$\frac{1}{2} \div ab^2 \cdot 9(-4b^5)$$. 2. **Rewrite division as multiplication:** Division by $$ab^2$$ is the same as multiplication by its reciprocal: $$\frac{1}{2} \div ab^2 = \frac{1}{2} \cdot \frac{1}{ab^2} = \frac{1}{2ab^2}$$. 3. **Substitute back:** The expression becomes $$\frac{1}{2ab^2} \cdot 9(-4b^5)$$. 4. **Multiply constants:** Multiply $$\frac{1}{2}$$, $$9$$, and $$-4$$: $$\frac{1}{2} \cdot 9 \cdot (-4) = \frac{1 \cdot 9 \cdot (-4)}{2} = \frac{-36}{2} = -18$$. 5. **Multiply variables:** Multiply $$\frac{1}{ab^2}$$ by $$b^5$$: $$\frac{b^5}{ab^2} = \frac{b^{5-2}}{a} = \frac{b^3}{a}$$. 6. **Combine results:** The simplified expression is $$-18 \cdot \frac{b^3}{a} = \frac{-18b^3}{a}$$. **Final answer:** $$\boxed{\frac{-18b^3}{a}}$$.