Question

Evaluate : `(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`

Answer 1

`(64)^(2/3) - root(3)(125) - 1/2^(-5) + (27)^(-2/3) xx (25/9)^(-1/2)`

= `(4^3)^(2/3) - root(3)(5^3) - 2^5 + (3^3)^(-2/3) xx ((5^2)/(3^2))^(-1/2)`

= `4^2 - 5 - 2^5 + 3^-2 xx (5/3)^( 2 xx (-1/2)`

= `16 - 5 - 32 + 1/3^2 xx (5/3)^-1`

= `- 21 + 1/9 xx 3/5`

= `- 21 + 1/15`

= `[ - 315 + 1 ]/15`

= `- 314/15`

= `- 20 14/15`