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Question
Simplify the following:
`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`
Solution
`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`
= `(3^4)^(3/4) - (1/2^5)^((-2)/5) + (2^3)^(1/3). (1/2)^-1 xx 1` ......(Using a0 = 1)
= `3^(4xx3/4) - (1)/(2^(5xx(-2/5))) + 2^(3xx1/3) .(2)^1` ......(Using (am)n = amn)
= `3^3 - (1)/(2^-2) + 2^1 . (2)^1`
= 33 - 22 + 21 + 1 .....`("Using" "a"^"m" xx "a"^"n" = "a"^"m+n" and "a"^-"n" = 1/"a"^"n")`
= 33 - 22 + 22
= 27.
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