I would like to know if the following are correct and if not how and what did I do wrong.

Question

27^-2/3
27^-1/3 = 27^-2/3 - -1/3 = 27^-3/3 sqrt 27

(a^1/2b)^1/2 (ab^1/2) = a^5/4b

Answer 1

since 27 = 3^3,
27^(1/3) = 3
27^(2/3) = 3^2 = 9
So, you have
27^-(2/3) = 1/27^(2/3) = 1/9

the other is correct

Answer 2

Thank you Steve