1. **State the problem:** Evaluate the expression $$9^{-\frac{3}{2}}$$. 2. **Recall the rules:** For any positive number $a$ and rational exponent $m/n$, $$a^{\frac{m}{n}} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m$$. 3. **Rewrite the expression:** $$9^{-\frac{3}{2}} = \frac{1}{9^{\frac{3}{2}}}$$ because of the negative exponent rule $a^{-b} = \frac{1}{a^b}$. 4. **Evaluate the denominator:** $$9^{\frac{3}{2}} = \left(9^{\frac{1}{2}}\right)^3 = (\sqrt{9})^3 = 3^3 = 27$$. 5. **Combine the results:** $$9^{-\frac{3}{2}} = \frac{1}{27}$$. **Final answer:** $$\boxed{\frac{1}{27}}$$