TITLE: Show that $8^{1/\pi}$ has infinitely many values.
QUESTION [8 upvotes]: Show that $8^{1/\pi}$ has infinitely many values. If it were possible to plot all its values, what would the picture look like. 
How do I go about solving this.

REPLY [2 votes]: Hint: $a^b = \exp(b \log a)$.   The values of $\log a$ are $y + 2 \pi i n$ where $y$ is one value and $n$ is an arbitrary integer.