To determine which option is equivalent to \( \frac{1}{8^5} \), we can rewrite \( \frac{1}{8^5} \) using negative exponents.
Recall that:
\[ \frac{1}{a^n} = a^{-n} \]
Applying this here:
\[ \frac{1}{8^5} = 8^{-5} \]
Now, let's look at the options provided:
- 8 1/2 - This is not a mathematical expression we need.
- 8^5 - This is not equivalent; it is \( 8^5 \) itself.
- 8^-5 - This is equivalent to \( \frac{1}{8^5} \).
- 5^-8 - This is not equivalent to \( \frac{1}{8^5} \).
The correct answer is:
8^-5.