How many solutions does $1=x^π$ have? I was wondering how many solutions there are to $1 = x^\text{irrational number}$, since the cube root of 1 has 3 solutions and the 4th root has 4 etc and since the number of solutions to $x = x^{a/b}$ is b (where $a$ and $b$ share no factors), how many would $x^π=1$ have? Infinity, none or something else?

$$1^\pi=e^{\pi(\ln1+2k\pi i)}=e^{i2k\pi^2}\hspace{1cm}k\in\mathbb{Z}$$
