The iteration of exponents laws I learned gives: $$i^{4/3}=i^{4\cdot1/3}=(i^{4})^{1/3}=1^{1/3}=1$$ I know this is wrong but now the iteration of exponents laws I have used over the years somehow doesn't apply or is flawed. This is quite embarrassing as I have been studying mathematics for quite some time now. Please help.
I know there is something wrong with this but I don't know where. It's some kind of a math fallacy and it is driving me crazy. Here it is: $$-1= (-1)^3 = (-1)^{6/2} = \sqrt{(-1)^6}= 1?$$
Why is this true?  $(\exists x)(P(x) \Rightarrow (\forall y) P(y))$