Question

Which of the following is developed to be equivalent to 1/8^5 ?(1 point)
Responses

5−8
5 superscript negative 8 baseline

85
8 superscript 5 baseline

815

Answer 1

To find an equivalent expression for \( \frac{1}{8^5} \), we can rewrite it using the properties of exponents.

1. The expression \( \frac{1}{8^5} \) can be rewritten using negative exponents:
\[
\frac{1}{8^5} = 8^{-5}
\]

Now let's analyze the responses:

1. \( 5^{-8} \) - This is not equivalent to \( \frac{1}{8^5} \).
2. \( 8^5 \) - This is just \( 8^5 \), not equivalent either.
3. \( 8^{15} \) - This does not match either.
4. \( 8^{-5} \) - This is equivalent to \( \frac{1}{8^5} \).

So the correct response, if it were provided (which seems like it might be a formatting issue), would be \( 8^{-5} \).

If you must choose from the given options and considering \( 5^{-8} \), \( 8^5 \), and \( 815 \) do not correspond to \( \frac{1}{8^5} \), then none of the answers listed directly reflect \( \frac{1}{8^5} \).

Please check to see if the option representing \( 8^{-5} \) might be incorrectly represented or missing, as this is the only equivalent form to the expression given.