Example: $$z^\pi =27$$ with $z \in \mathbb{C}$
$$z=27^{\left(\frac{1}{\pi}\right)}=(r \, e^{i\phi+k2\pi i})^{\left(\frac{1}{\pi}\right)}=r \, e^{\frac{i\phi}{\pi}+k2 i}$$ for $k \in \mathbb{Z}$.
I believe this should mean that the equation has infinite solutions because $$\frac{i\phi}{\pi} + 2 \, k \, i \neq t \pi$$ for $t \in \mathbb{Z}$. Am I correct?