1. **State the problem:** Simplify the expression $ (4^3)^5 $. 2. **Use the power of a power rule:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \times n} $$ 3. **Apply the rule:** $$ (4^3)^5 = 4^{3 \times 5} = 4^{15} $$ 4. **Calculate the final value:** Since $4 = 2^2$, rewrite $4^{15}$ as $$ 4^{15} = (2^2)^{15} = 2^{2 \times 15} = 2^{30} $$ 5. **Evaluate $2^{30}$:** $$ 2^{30} = 1073741824 $$ **Final answer:** $$ (4^3)^5 = 4^{15} = 1073741824 $$