Question

Which of the following is developed to be equivalent to 1/8 of the 5th power

Answer 1

To express \( \frac{1}{8} \) in terms of the 5th power, we first note that \( \frac{1}{8} = 8^{-1} \), and since \( 8 = 2^3 \), we can express \( \frac{1}{8} \) as:

\[
\frac{1}{8} = 2^{-3}
\]

Now, we want to find the 5th power of \( \frac{1}{8} \):

\[
\left( \frac{1}{8} \right)^5 = \left( 2^{-3} \right)^5
\]

Using the power of a power property of exponents \( (a^m)^n = a^{m \cdot n} \), we get:

\[
\left( 2^{-3} \right)^5 = 2^{-15}
\]

Thus, \( \left( \frac{1}{8} \right)^5 \) is equivalent to \( 2^{-15} \).

So, \( \frac{1}{8} \) raised to the 5th power is equivalent to \( 2^{-15} \). Hence, \( \frac{1}{8} \) of the 5th power can be expressed as \( 2^{-15} \).