To evaluate \( 2 \cdot 8^{-2} \), we first simplify \( 8^{-2} \).
Recall that \( a^{-n} = \frac{1}{a^n} \). Thus, we have:
\[ 8^{-2} = \frac{1}{8^2} \]
Next, we calculate \( 8^2 \):
\[ 8^2 = 64 \]
So,
\[ 8^{-2} = \frac{1}{64} \]
Now substitute this back into the original expression:
\[ 2 \cdot 8^{-2} = 2 \cdot \frac{1}{64} \]
We can multiply these numbers:
\[ 2 \cdot \frac{1}{64} = \frac{2}{64} \]
Now, we simplify \( \frac{2}{64} \):
\[ \frac{2}{64} = \frac{1}{32} \]
Thus, the final answer is:
\[ \boxed{\frac{1}{32}} \]