Question

Write this as fraction or integer without a power:
(1(1/2))^-3

Answer 1

To rewrite \((1(1/2))^{-3}\) as a fraction or integer without a power, we first interpret it clearly. The expression can be read as \((1 \cdot \frac{1}{2})^{-3}\), which simplifies to \(\left(\frac{1}{2}\right)^{-3}\).

Now, we can handle the negative exponent:

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

Calculating \(\left(\frac{1}{2}\right)^3\):

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

So now we have:

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

Thus, \((1(1/2))^{-3}\) simplifies to:

\[
\boxed{8}
\]