1. **State the problem:** Simplify the expression $$(4h^5)^3$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power separately: $$ (ab)^n = a^n b^n $$ 3. **Apply the rule:** $$ (4h^5)^3 = 4^3 \cdot (h^5)^3 $$ 4. **Calculate each part:** - $4^3 = 4 \times 4 \times 4 = 64$ - For powers of powers, multiply exponents: $$ (h^5)^3 = h^{5 \times 3} = h^{15} $$ 5. **Combine the results:** $$ (4h^5)^3 = 64h^{15} $$ **Final answer:** $$ 64h^{15} $$