1. The problem is to simplify the expression $$\frac{81}{9^{2 - 3x}}$$ given that $$y = 3^x$$. 2. First, express 81 and 9 in terms of base 3 because 81 and 9 are powers of 3: $$81 = 3^4$$ and $$9 = 3^2$$. 3. Rewrite the denominator using the base 3 expression: $$9^{2 - 3x} = (3^2)^{2 - 3x} = 3^{2(2 - 3x)} = 3^{4 - 6x}$$. 4. Now the expression becomes: $$\frac{3^4}{3^{4 - 6x}}$$. 5. Use the rule for division of exponents with the same base: $$\frac{a^m}{a^n} = a^{m-n}$$. 6. Apply this rule: $$3^{4 - (4 - 6x)} = 3^{4 - 4 + 6x} = 3^{6x}$$. 7. Since $$y = 3^x$$, then $$3^{6x} = (3^x)^6 = y^6$$. **Final answer:** $$\frac{81}{9^{2 - 3x}} = y^6$$.