1. **State the problem:** Simplify the expression $(-4a^{-5}) \cdot (2a^{-6}b^{0})$ and identify the correct multiple-choice answer. 2. **Recall the rules:** - When multiplying terms with the same base, add the exponents: $a^m \cdot a^n = a^{m+n}$. - Any number to the zero power is 1: $b^0 = 1$. - Multiply coefficients normally. 3. **Apply the rules:** - Multiply coefficients: $-4 \times 2 = -8$. - Add exponents of $a$: $-5 + (-6) = -11$. - Since $b^0 = 1$, it does not affect the product. 4. **Write the simplified expression:** $$-8a^{-11}$$ 5. **Match with the options:** - Option D is $-8 / a^{11}$, which is equivalent to $-8a^{-11}$. **Final answer:** Option D: $-8 / a^{11}$