This is a question about the imaginary roots of the two equations
$$
(-256)^{\frac{1}{4}} \qquad\text{and}\qquad 1^{\frac{1}{5}}.
$$
For the first one I've worked out that 2 of the solutions are $4\sqrt{\mathrm{i}}$ and $-4\sqrt{\mathrm{i}}$; but I thought the other two solutions would lie on the real axis and be $+4$ and $-4$.
These were incorrect.
What would the other two solutions be and why?

For the second one I found one of the solutions, which is $1$. There are another 4 solutions that I have no clue how to find.

I've found the solutions for (2): $1$, $\mathrm{e}^{\frac{2}{5}\pi\mathrm{i}}$, $\mathrm{e}^{\frac{2}{5}\pi\mathrm{i}}$, $\mathrm{e}^{\frac{4}{5}\pi\mathrm{i}}$, $\mathrm{e}^{-\frac{2}{5}\pi\mathrm{i}}$, $\mathrm{e}^{-\frac{4}{5}\pi\mathrm{i}}$.
The third one is apparently incorrect. Why is this?