Questions: Rewrite the given expression in the form (2^mathrmu) where u is a constant or an algebraic expression. [ frac12^3 ] [ frac12^3= ] (Type your answer using exponential notation.)

Solution Steps

To rewrite the expression \(\frac{1}{2^3}\) in the form \(2^{\mathrm{u}}\), we need to use the property of exponents that states \(a^{-b} = \frac{1}{a^b}\). Therefore, \(\frac{1}{2^3}\) can be rewritten as \(2^{-3}\).

We start with the expression

\[ \frac{1}{2^3} \]

To rewrite this in the form \(2^{\mathrm{u}}\), we apply the property of exponents:

\[ \frac{1}{a^b} = a^{-b} \]

Thus, we can express \(\frac{1}{2^3}\) as:

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

Next, we evaluate the original expression:

\[ \frac{1}{2^3} = \frac{1}{8} = 0.125 \]

We have rewritten the expression as \(2^{-3}\). To confirm, we can evaluate \(2^{-3}\):

\[ 2^{-3} = \frac{1}{2^3} = \frac{1}{8} = 0.125 \]

Both forms are equivalent.

Final Answer