Anything raised to the zero is 1... so it doesn't really matter what is in the parentheses, because it's all raised to the zero and equals 1. That means..
(t^1/3 - t^5/3 + t^3/4)^0 = 2 root t
is the same as
1 = 2 root t square both sides
1^2 = (2 root t)^2
1 = 4t divide each side by 4
1/4 = t
