Which of the following is developed to be equivalent to 1/8^5?

Question

8 1/2
8^5
8^-5
5^-8

Answer 1

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:

1. 8 1/2 - This is not a mathematical expression we need.
2. 8^5 - This is not equivalent; it is \( 8^5 \) itself.
3. 8^-5 - This is equivalent to \( \frac{1}{8^5} \).
4. 5^-8 - This is not equivalent to \( \frac{1}{8^5} \).

The correct answer is:

8^-5.