1. **State the problem:** Simplify the expression $$(3m^{-4})^3(3m^5)$$ and find which option it is equivalent to. 2. **Recall the exponent rules:** - Power of a power: $$(a^m)^n = a^{mn}$$ - Product of powers with the same base: $$a^m \cdot a^n = a^{m+n}$$ - Negative exponent: $$a^{-m} = \frac{1}{a^m}$$ 3. **Apply the power of a power rule:** $$(3m^{-4})^3 = 3^3 \cdot (m^{-4})^3 = 27m^{-12}$$ 4. **Multiply by the second term:** $$27m^{-12} \cdot 3m^5 = 27 \cdot 3 \cdot m^{-12 + 5} = 81m^{-7}$$ 5. **Rewrite with positive exponents:** $$81m^{-7} = \frac{81}{m^7}$$ 6. **Final answer:** The expression is equivalent to $$\frac{81}{m^7}$$ which corresponds to options A and D. Since both A and D are the same, the correct answer is **A. 81/m^7**.