Solve for t in the equation below

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