1. Let's solve the first problem: Calculate $9^{-3/2}$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$ and $a^{-b} = \frac{1}{a^b}$. 3. Rewrite $9^{-3/2}$ as $(3^2)^{-3/2}$ because $9 = 3^2$. 4. Apply the power of a power rule: $(3^2)^{-3/2} = 3^{2 \times (-3/2)} = 3^{-3}$. 5. Use the negative exponent rule: $3^{-3} = \frac{1}{3^3} = \frac{1}{27}$. 6. Therefore, the final answer is $\frac{1}{27}$.