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Question
When simplified \[(256) {}^{- ( 4^{- 3/2} )}\] is
Options
8
\[\frac{1}{8}\]
2
\[\frac{1}{2}\]
Solution
Simplify `(256)^((-4 3/2)`
`(256)^((-4 3/2))` = `(256)^-(2^2)^(3/2)`
= `(256)^((-2^(2xx - 3/2))`
= `(256)^-(2^(2xx - 3/2))`
`(256)^((-4-^(3/2))` = `(256)^(-(2) ^((-3))`
`(256)^((-4-^(3/2))` = `(256) ^(1/((-2))`
= `(256) ^(1/(-8)`
= `(2^8) ^(1/(-8)`
= `2^(8 xx 1/(-8)`
`(256)^((-4 -3/2)) = 2^(8xx 1/-8) = 1/2`
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