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Question
Simplify:
`(256)^(-(4^((-3)/2))`
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Solution
`(256)^(-(4^(-3/2))) = (256)^(-(4)^(-3/2)`
= `(256)^(-(2^2)^(-3/2))`
= `(256)^(-(2^(2 xx -3/2))` ...`[∵ b^((a^m)^n) = b^(a^(mn))]`
= `(256)^(-(2^-3))`
= `(2^8)^(-(1/2^3)`
= `(2^8)^(-1/8)`
= `2^(8 xx -1/8)`
= `2^-1`
= `1/2`
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