When answering this question, I contemplated across the following problem:
Find $x$ such that $x^{\frac{1}{x}}=0.$
I thought RHS $ = 0$ is a special case, so I attempted solving $\frac{1}{x} \ln x = \ln c$ from some constant $c > 0,$ but I do not know how. I heard about Lambert W, but I am not familiar with it.
BTW, Maple solve(x^(1/x) = 0)
gives $x=0$, and WolframAlpha gives (no solution exist)
!
How can I solve this?