1. **State the problem:** Simplify and evaluate $\frac{(6^2)^8}{(6^4)^2}$. 2. **Recall exponent laws:** - Power of a power: $(a^m)^n = a^{m \times n}$ - Division of same base: $\frac{a^m}{a^n} = a^{m-n}$ 3. **Apply power of a power:** $$(6^2)^8 = 6^{2 \times 8} = 6^{16}$$ $$(6^4)^2 = 6^{4 \times 2} = 6^{8}$$ 4. **Rewrite the expression:** $$\frac{6^{16}}{6^{8}}$$ 5. **Apply division rule for exponents:** $$6^{16-8} = 6^{8}$$ 6. **Evaluate $6^8$:** Calculate stepwise: $6^2 = 36$ $6^4 = (6^2)^2 = 36^2 = 1296$ $6^8 = (6^4)^2 = 1296^2 = 1,679,616$ **Final answer:** $$6^8 = 1,679,616$$