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#.