How do you simplify $2^{3} - 2^{- 1}$ $2^3 - 2^-1$ ?

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How do you simplify $2^{3} - 2^{- 1}$ $2^3 - 2^-1$ ?

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Answer 1 · 2015-10-03T18:11:07

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

Explanation:

$2^{3} = 2 \times 2 \times 2 = 8$ $color(red)(2^3) = 2xx2xx2 = color(red)(8)$
and
$2^{- 1} = \frac{1}{2^{1}} = \frac{1}{2}$ $color(blue)(2^(-1)) = 1/(2^(1)) = color(blue)(1/2)$

So
$2^{3} - 2^{- 1} = 8 - \frac{1}{2} = 7 \frac{1}{2}$ $color(red)(2^3) - color(blue)(2^(-1)) = color(red)(8) - color(blue)(1/2) = 7 1/2$

Answer 2 · 2015-10-03T18:13:04

7.5

Explanation:

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

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

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

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

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