1. **State the problem:** Simplify the expression $$(4g^5)^2$$. 2. **Recall the power of a product rule:** When raising a product to a power, raise each factor to that power separately. That is, $$(ab)^n = a^n b^n$$. 3. **Apply the rule:** $$(4g^5)^2 = 4^2 \cdot (g^5)^2$$. 4. **Simplify each part:** $$4^2 = 16$$ $$(g^5)^2 = g^{5 \times 2} = g^{10}$$. 5. **Combine the results:** $$16g^{10}$$. **Final answer:** $$16g^{10}$$.