Question

Which of the following is developed to be equivalent to one eighth to the fifth power?

1. eight to the fifth power
2. five to the negative eighth power
3. eight to the negative fifth power
4. eight one fifths

Answer 1

To find which option is equivalent to one eighth to the fifth power, we first need to express one eighth in mathematical form:

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

If we raise \(\frac{1}{8}\) to the fifth power, we have:

\[
\left(\frac{1}{8}\right)^5 = (8^{-1})^5 = 8^{-5}
\]

Now, let's evaluate the options:

1. **eight to the fifth power**: \(8^5\) (not equivalent)
2. **five to the negative eighth power**: \(5^{-8}\) (not equivalent)
3. **eight to the negative fifth power**: \(8^{-5}\) (this is equivalent)
4. **eight one fifths**: \(8 \frac{1}{5}\) or simply a mixed number (not equivalent)

The correct answer is:

**3. eight to the negative fifth power**