1. **State the problem:** Simplify the expression $$\frac{x^2 y^3}{x^9 y^{-6}}$$ and express it in the form $$\frac{y^{[?]}}{x^{[?]}}$$. 2. **Recall the division rule for exponents:** When dividing like bases, subtract the exponents: $$\frac{a^m}{a^n} = a^{m-n}$$. 3. **Apply the rule to the x terms:** $$\frac{x^2}{x^9} = x^{2-9} = x^{-7}$$. 4. **Apply the rule to the y terms:** $$\frac{y^3}{y^{-6}} = y^{3 - (-6)} = y^{3+6} = y^9$$. 5. **Rewrite the expression:** $$\frac{x^{-7} y^9}{1} = y^9 x^{-7}$$. 6. **Express with positive exponents in denominator:** Since $$x^{-7} = \frac{1}{x^7}$$, the expression becomes $$\frac{y^9}{x^7}$$. 7. **Final answer:** $$\frac{y^9}{x^7}$$. Thus, the exponent for y is 9 and for x is 7.