Question

Simplify the following:

`(81)^(3/4) - (1/32)^(-2/5) + 8^(1/3).(1/2)^-1. 2^0`

Answer 1

`(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 (a^m)ⁿ = a^mn)

= `3^3 - (1)/(2^-2) + 2^1 . (2)^1`

= 3³ - 2² + 2^{1 + 1}    .....`("Using"  "a"^"m" xx "a"^"n" = "a"^"m+n" and "a"^-"n" = 1/"a"^"n")`
= 3³ - 2² + 2²
= 27.