Algebra 2

27^(4/3) =

(27^4)^1/3 =

(531,441)^1/3 =81 - It is 27 to the 4th power and then take the cube root.

4^3/2 =

(4^3)^1/2 =

(64)^1/2 = 8 - it is the cube of 4 and then take the square root.

For the first one, it would have been easier computationally speaking if you rewrote $\left(\sqrt[3]{27}\right)^4=3^4=3*3*3*3=9*9=81$