To determine which of the given responses is equivalent to \( \frac{1}{8^{5}} \), we can rewrite \( \frac{1}{8^{5}} \) in exponential form.
Using the negative exponent rule, we have:
\[ \frac{1}{8^{5}} = 8^{-5} \]
Now let's review the responses:
- \( 8 \cdot \frac{1}{5} \)
- \( 8^{-5} \)
- \( 8^{5} \)
- \( 5^{-8} \)
The correct answer is:
\( 8^{-5} \).