The problem is to simplify the expression $(-3 \cdot (-6))^{-3}$.

1. Problem Description

The problem is to simplify the expression $(-3 \cdot (-6))^{-3}$.

2. Solution Steps

First, we simplify the expression inside the parentheses:

$-3 \cdot (-6) = 18$.

So the expression becomes $(18)^{-3}$.

Using the rule $a^{-n} = \frac{1}{a^n}$, we have:

$(18)^{-3} = \frac{1}{18^3}$.

Now we calculate $18^3$:

$18^3 = 18 \cdot 18 \cdot 18 = 324 \cdot 18 = 5832$.

Therefore, the expression simplifies to:

$\frac{1}{5832}$.

3. Final Answer

$\frac{1}{5832}$