1. **State the problem:** Evaluate the expression $$\frac{x^{-2}}{y^{-2}}$$ when $$x=3$$ and $$y=-4$$. 2. **Recall the rule for negative exponents:** $$a^{-n} = \frac{1}{a^n}$$ for any nonzero number $$a$$ and positive integer $$n$$. 3. **Rewrite the expression using positive exponents:** $$\frac{x^{-2}}{y^{-2}} = \frac{\frac{1}{x^2}}{\frac{1}{y^2}}$$ 4. **Divide the fractions:** $$= \frac{1}{x^2} \times \frac{y^2}{1} = \frac{y^2}{x^2}$$ 5. **Substitute the given values:** $$= \frac{(-4)^2}{3^2}$$ 6. **Calculate powers:** $$= \frac{16}{9}$$ 7. **Final answer:** $$\frac{x^{-2}}{y^{-2}} = \frac{16}{9}$$ This fraction is already in simplest form.