To solve the expression $9 \cdot 3^{-3}$, we need to first deal with the exponent and then multiply.

The expression $3^{-3}$ means $\frac{1}{3^3}$. Calculating $3^3$, we have:

$3^3 = 3 \cdot 3 \cdot 3 = 27$

Thus, $3^{-3} = \frac{1}{27}$.

Now, multiply $9$ by $\frac{1}{27}$:

$9 \cdot \frac{1}{27} = \frac{9}{27}$

Simplify $\frac{9}{27}$ by dividing both the numerator and the denominator by 9:

$\frac{9}{27} = \frac{1}{3}$

Therefore, the result of $9 \cdot 3^{-3}$ is $\frac{1}{3}$.