1. **State the problem:** Simplify the expression $\frac{1}{2}a^{3}b \div ab^{2} \cdot (-4b^{5})$. 2. **Rewrite the expression:** Division can be rewritten as multiplication by the reciprocal: $$\frac{1}{2}a^{3}b \times \frac{1}{ab^{2}} \times (-4b^{5})$$ 3. **Multiply the coefficients:** $$\frac{1}{2} \times 1 \times (-4) = -2$$ 4. **Multiply the variables with the same base by adding exponents:** - For $a$: $a^{3} \times a^{-1} = a^{3-1} = a^{2}$ - For $b$: $b^{1} \times b^{-2} \times b^{5} = b^{1-2+5} = b^{4}$ 5. **Combine the results:** $$-2a^{2}b^{4}$$ **Final answer:** $$-2a^{2}b^{4}$$