Is there any notation for general $n$-th root $r$ such that $r^n=x$? As we know that the notation for the $n$-th principal root is $\sqrt[n]{x}$ or $x^{1/n}$. But the principal root is not always the only possible root, e.g. for even $n$ and positive $x$ the principal root is always positive but there is also another negative root. E.g. consider $r^2=4$, then $\sqrt 4 =+2$, but $r=-2$ is also a valid solution. Since $x$ is a function of $r$ for some given $n$, so let 
$$r^n=x=f(r).$$
We have $r=f^{-1} (x)$. Here $r \neq \sqrt[n]x$ because $\sqrt[n]x$ is the principal root not the general. So is there any notation like $\sqrt[n]{\phantom{aa}}$ for the general $n$-th root of the equation $r^n=x$?

In complex analysis, $\sqrt[n]{x}$ is regarded as a multivalued function. Or you can write it as $$\sqrt[n]{x}=\exp{\frac{\operatorname{Log}(x)}{n}},\space x\ne0.$$
$\operatorname{Log}(x)$ is the inverse function of $\exp(x)$, see here.
