If base is less than 0 then it function is which type??

Example:- (-8)^1/3

this is an important ques. actually, if we define f(x)= a^x, such that a is less than zero, then f would neither be continuous nor differentiable. that is why no special name is given to such function. it is only when a is greater than zero that f becomes continuous and differentiable, and hence called exponential function. we can draw its graph too.

 f(x)= a^x, such that a is less than zero, is not continuous because when x= some fractional value like ½ , then the value of the function does not exist in real numbers.