The domain is the subset of R for which all operations in the function’s formula make sense.
Since e is a positive real constant, it can be raised to any real power, so the domain is not limited. It is R.
The range is the set of function’s values.
Since a positive real constant is raised to a real power, the result is always positive, and is never equal to zero (if the power is to equal zero its base must equal zero, and its exponent must be different from zero). So the range is all positive real numbers without zero (0;+∞)
The domain is R, the range is (0;+∞)