1. **State the problem:** Calculate $$\frac{3^2 \times 3}{3^4 + 3 \times 27}$$. 2. **Recall the rules:** - When multiplying powers with the same base, add the exponents: $$a^m \times a^n = a^{m+n}$$. - Evaluate powers and simplify step-by-step. 3. **Calculate the numerator:** $$3^2 \times 3 = 3^2 \times 3^1 = 3^{2+1} = 3^3 = 27$$. 4. **Calculate the denominator:** - First, calculate $$3^4 = 81$$. - Then calculate $$3 \times 27 = 81$$. - Sum them: $$81 + 81 = 162$$. 5. **Form the fraction:** $$\frac{27}{162}$$. 6. **Simplify the fraction:** Divide numerator and denominator by 27: $$\frac{27 \div 27}{162 \div 27} = \frac{1}{6}$$. **Final answer:** $$\frac{1}{6}$$ which corresponds to option D.