# How do you simplify 2^3 - 2^-1?

Oct 3, 2015

${2}^{3} - {2}^{- 1} = 7.5$

#### Explanation:

$\textcolor{red}{{2}^{3}} = 2 \times 2 \times 2 = \textcolor{red}{8}$
and
$\textcolor{b l u e}{{2}^{- 1}} = \frac{1}{{2}^{1}} = \textcolor{b l u e}{\frac{1}{2}}$

So
$\textcolor{red}{{2}^{3}} - \textcolor{b l u e}{{2}^{- 1}} = \textcolor{red}{8} - \textcolor{b l u e}{\frac{1}{2}} = 7 \frac{1}{2}$

Oct 3, 2015

7.5

#### Explanation:

First, remove the negative exponent. You can do this by getting the reciprocal of the base.
2^3−2^(−1)
=2^3−1/2^1

Next, get the cube of ${2}^{3}$.
2^3−1/2
=8−1/2

Subtract 1/2 from 8.
8−1/2
=16/2−1/2
$= \frac{16 - 1}{2}$
$\textcolor{red}{= \frac{15}{2}}$

The answer is $\frac{15}{2}$ or $7.5$.