To find out which of the options is equivalent to \( \frac{1}{8^5} \), we can start by rewriting \( \frac{1}{8^5} \) in exponential form.
The expression can be rewritten as: \[ 8^{-5} \] because \( \frac{1}{a^b} = a^{-b} \).
Now let's evaluate the options one by one:
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\( 8^5 \): This is simply \( 8 \) raised to the power of \( 5 \), which is not equivalent to \( \frac{1}{8^5} \).
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\( 8^{-5} \): This expression is exactly what we found equivalent to \( \frac{1}{8^5} \).
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\( 81/5 \): This is a fraction and is not equivalent to \( \frac{1}{8^5} \).
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\( 5^{-5} \): This expression is \( \frac{1}{5^5} \), which is not equivalent to \( \frac{1}{8^5} \).
Therefore, the correct option that is equivalent to \( \frac{1}{8^5} \) is:
\( 8^{-5} \).