We all know that many years ago we invented powers. e.g. $3^4$ meant how many times we multiply 3. i.e. $3^4=3\cdot 3\cdot 3\cdot 3$.
But then, people started asking questions like what is the meaning of $3^{-4}$, or $3^{\frac{1}{4}}$ and so forth. Same goes for factorial. People wanted to determine what is the meaning of $2.3!$ or $-\pi !$, and so forth.
By the same logic, I started wondering what can be the meaning of $^{\frac{1}{2}}2$, or $^{-3}4$, or even $^i3$, and could not come up with an answer, or something close to one.
Does someone have an idea that can be used to determine what $^{-3}4$ would be?
EDIT: Note that I read about the subject on Wikipedia, and this stackexchange question: How would tetration work for non integer numbers.. I wanted to see if someone else had an idea.
