The problem is to evaluate the expression $\frac{1}{2} \cdot (-\frac{1}{2})^2 + \sqrt{\frac{1}{64}}$.

1. Problem Description

The problem is to evaluate the expression $\frac{1}{2} \cdot (-\frac{1}{2})^2 + \sqrt{\frac{1}{64}}$.

2. Solution Steps

First, evaluate $(-\frac{1}{2})^2$:

$(-\frac{1}{2})^2 = (-\frac{1}{2}) \cdot (-\frac{1}{2}) = \frac{1}{4}$

Next, evaluate $\frac{1}{2} \cdot (\frac{1}{4})$:

$\frac{1}{2} \cdot \frac{1}{4} = \frac{1}{8}$

Then, evaluate $\sqrt{\frac{1}{64}}$:

$\sqrt{\frac{1}{64}} = \frac{\sqrt{1}}{\sqrt{64}} = \frac{1}{8}$

Finally, add the two terms:

$\frac{1}{8} + \frac{1}{8} = \frac{2}{8} = \frac{1}{4}$

3. Final Answer

$\frac{1}{4}$