Whenever I ask GeoGebra to draw a graph of $x^{(\mathrm{integer}_1, \mathrm{integer}_2)}$
it outputs a strange structure for which I have no more rigorous description than a "bar-like spiral".
The following picture will, hopefully, provide better insight.
I am not aware that something else than a scalar can be used as an exponent. If yes, what is it? Interval? Vector? Or is the whole thing just some GeoGebra's quirk?
It appears that the notation $$ f(x) = x^{m,n} $$ (with optional parentheses around $m,n$) is interpreted as the complex function $$ f(x) = x^{m + ni}. $$ Then, the image of the square grid from $-10 - 10i$ to $10 + 10i$ is plotted as a 2D graph.
Here are a few examples.
$$ f(x) = x^{1,0} $$
$$ f(x) = x^{2,0} $$
$$ f(x) = x^{1,1} $$
$$ f(x) = x^{-3,0} $$