Does the zeroth root exist? Definition of $Nth$ root:
$3rd$ order inverse group $1$ hyperoperation.
Division is how many times you can subtract a certain divisor from the dividend before it becomes negative.
Likewise Nth root is the result of repeated division by a certain divisor before it becomes $1$ or a decimal. The number of times you divide it before it becomes a decimal is the index.
Ex: $\sqrt [3]{8} = (8/2)/2$
Is the zeroth root even defined and if so what is $\sqrt [0]{x}$

If we reform this, it could be represented as $X^{\frac{1}{0}}$, so when used in standard functional mathematics, it would be undefined, because $\frac{1}{0}$ is undefined.
However, if used in the calculation of a limit and the function reduces to this form after substitution, I'd think this would be considered an indeterminate form, because not enough information is given to determine the original limit.  It could be any number.  It would end up then looking like $1^\infty$, which would itself be an indeterminate form.
