The problem is to evaluate the expression $(\frac{1}{6})^2 \cdot (\frac{1}{2})^3$.

1. Problem Description

The problem is to evaluate the expression $(\frac{1}{6})^2 \cdot (\frac{1}{2})^3$.

2. Solution Steps

First, evaluate $(\frac{1}{6})^2$.

$(\frac{1}{6})^2 = \frac{1}{6} \cdot \frac{1}{6} = \frac{1}{36}$

Next, evaluate $(\frac{1}{2})^3$.

$(\frac{1}{2})^3 = \frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}$

Now, multiply the two results together.

$\frac{1}{36} \cdot \frac{1}{8} = \frac{1}{36 \cdot 8} = \frac{1}{288}$

3. Final Answer

The final answer is $\frac{1}{288}$.