To determine which of the provided options is equivalent to 185, we need to evaluate each expression:
- \( 85 \): This is just 85.
- \( 8^5 \): This equals \( 32768 \) (since \( 8 \times 8 \times 8 \times 8 \times 8 = 32,768 \)).
- \( 815 \): This is just 815.
- \( \frac{1}{5} 8^{-5} \): This can be rewritten as \( \frac{1}{5} \cdot \frac{1}{8^5} = \frac{1}{5 \cdot 32768} \) which is a very small number.
- \( 8^{-5} \): This is equal to \( \frac{1}{8^5} = \frac{1}{32768} \), which is also a very small number.
- \( 5^{-8} \): This equals \( \frac{1}{5^8} \), which is also a very small number.
None of these options are equivalent to 185. If one of these should be equivalent to 185, it isn't visible among the choices provided. Please double-check the original expressions for any mistakes or request further clarification if necessary.