1. **State the problem:** Simplify and evaluate the expression $$\frac{(3^2)^4}{3 \times 3 \times 3^4}$$. 2. **Recall exponent rules:** - Power of a power: $$ (a^m)^n = a^{m \times n} $$ - Product of powers with the same base: $$ a^m \times a^n = a^{m+n} $$ - Division of powers with the same base: $$ \frac{a^m}{a^n} = a^{m-n} $$ 3. **Simplify the numerator:** $$ (3^2)^4 = 3^{2 \times 4} = 3^8 $$ 4. **Simplify the denominator:** $$ 3 \times 3 \times 3^4 = 3^1 \times 3^1 \times 3^4 = 3^{1+1+4} = 3^6 $$ 5. **Rewrite the expression:** $$ \frac{3^8}{3^6} $$ 6. **Apply division rule:** $$ 3^{8-6} = 3^2 $$ 7. **Evaluate the final expression:** $$ 3^2 = 9 $$ **Final answer:** The simplified expression is $$3^2$$ and its value is 9. **Note:** The answer $$3^1$$ is incorrect; the correct simplification yields $$3^2$$.