# Show that $8^{1/\pi}$ has infinitely many values.

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.

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books.google.co.in/… –  lab bhattacharjee Sep 28 '12 at 7:38

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.