Because taking the 2/3rd power of something is equivalent to taking the cube root, then squaring (or squaring, then taking the cube root). So

27^2/3 = (27^(1/3))^2 = 3^2 = 9 or

27^2/3 = (27^(2))^1/3 = 729^1/3 = 9

Another way to see it is to write 27 as 3^(3). Then you can apply the same logic that transformed x^27 to x^(18).