1. **State the problem:** Simplify the expression $g = (5c^2 d^3)^4$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power: $$ (abc)^n = a^n b^n c^n $$ 3. **Apply the rule:** $$ (5c^2 d^3)^4 = 5^4 (c^2)^4 (d^3)^4 $$ 4. **Simplify each term:** - $5^4 = 625$ - $(c^2)^4 = c^{2 \times 4} = c^8$ - $(d^3)^4 = d^{3 \times 4} = d^{12}$ 5. **Combine all:** $$ 625 c^8 d^{12} $$ **Final answer:** $625 c^8 d^{12}$