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

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Answer 1 · 2015-10-03T18:11:07

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

$color(red)(2^3) = 2xx2xx2 = color(red)(8)$
and
$color(blue)(2^(-1)) = 1/(2^(1)) = color(blue)(1/2)$

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

Answer 2 · 2015-10-03T18:13:04

7.5

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.
$8−1/2$
$=16/2−1/2$
$=(16-1)/2$
$color(red)(=15/2)$

The answer is $15/2$ or $7.5$ .

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