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

Question

Responses

8−^5
8 superscript negative 5 baseline

8^1/5
8 Start Fraction 1 over 5 End Fraction

8^5
8 superscript 5 baseline

5^−8

Answer 1

To determine which expression is equivalent to \( \frac{1}{8^5} \), we can manipulate the options given.

The expression \( \frac{1}{8^5} \) can be rewritten using negative exponents:

\[ \frac{1}{8^5} = 8^{-5} \]

Now, let's check the provided options:

1. \( 8^{-5} \) – This is equivalent to \( \frac{1}{8^5} \).
2. \( 8^{1/5} \) – This is the fifth root of 8, which is not equivalent to \( \frac{1}{8^5} \).
3. \( 8^5 \) – This is simply \( 8^5 \) and not equivalent to \( \frac{1}{8^5} \).
4. \( 5^{-8} \) – This represents \( \frac{1}{5^8} \), which is also not equivalent to \( \frac{1}{8^5} \).

The correct answer is:

8−^5 (or \( 8^{-5} \))