I believe that the cubic root of $-8$ is $-2$, ie $\sqrt[3]{-8}=-2$, or $(-2)^3=-8$.
When I ask Maple to tell me what this cubic root is
root(-8, 3)
I get the result
$$2(-1)^{1/3}$$
In Maple, let's say that we want to plot $f(x)=\sqrt[3]{x}$
plot(x^(1/3), x = -2 .. 2)
The result is
Why don't we see the portion of the graph where $x<0$?
Here is another example, of $g(x)=\sqrt[3]{x^2-1}$. When I plot the function in Maple
plot((x^2 - 1)^(1/3), x = -2 .. 2)
There is no graph between $-1$ and $1$. I must be making a silly mistake, because in my mind $g(0)=-1$.
Is there a reason for Maple not to give the expected results for cubic roots of negative numbers?
See the Maple function
surd.plot(surd(x,3),x=-2..2);plot(surd(x^2 - 1,3), x = -2 .. 2);