Question

Evaluate the following:

`(64/216)^(2/3) xx (16/36)^(-3/2)`

Answer 1

`(64/216)^(2/3) xx (16/36)^(-3/2)`

= `(2^6/6^3)^(2/3) xx (2^4/6^2)^(-3/2)`

= `(2^6)^(2/3)/(6^3)^(2/3) xx (2^4)^(-3/2)/(6^2)^(-3/2)`

= `(2)^(6 xx 2/3)/(6)^(3 xx 2/3) xx (2)^(4 xx (-3/2))/(6^2)^(2 xx (-3/2))`        ......(Using (a^m)ⁿ = a^mn)

= `(2)^(2xx2)/(6)^2 xx (2)^(2 xx(-3))/(6)^-3`

= `(2)^4/(6)^2 xx (2)^-6/(6)^-3`        

= `(2)^4/(6)^2 xx (6)^3/(2)^6`    ......`("Using"  "a"^"m" = 1/"a"^"m")`

= = `(2)^4/(2)^6 xx (6)^3/(6)^2`

= `(2)^(4-6) xx (6)^(3 - 2)`     .....(Using a^m ÷ aⁿ = a^m-n)

= `(2)^-2 xx (6)^1`

= `(1)/(2^2) xx 6`

= `(1)/(4) xx 6`

= `(3)/(2)`.