1. **State the problem:** Simplify and evaluate $$\frac{(3^2)^4}{3 \times 3 \times 3^4}$$ and record the answer as an integer. 2. **Use the power of a power rule:** $$(a^m)^n = a^{m \times n}$$ 3. Apply this to the numerator: $$ (3^2)^4 = 3^{2 \times 4} = 3^8 $$ 4. Rewrite the denominator by combining the factors: $$ 3 \times 3 \times 3^4 = 3^1 \times 3^1 \times 3^4 = 3^{1+1+4} = 3^6 $$ 5. Now the expression is: $$ \frac{3^8}{3^6} $$ 6. Use the quotient rule for exponents: $$ \frac{a^m}{a^n} = a^{m-n} $$ 7. Simplify the fraction: $$ 3^{8-6} = 3^2 $$ 8. Evaluate the power: $$ 3^2 = 9 $$ **Final answer:** 9