It cannot be done (in a single step) on a basic calculator; but the search bar calculator is quite powerful.
You can type either ** or a ^ as the power symbol (operation). In other words, x**y and x^y means the same: x raised to the power of y.
If the power is integer you simply type it as such. For roots (say cube roots) you need to type 1/3 in parenthesis: 27^(1/3) will give you 3.
Internally, the numeric processor uses an algorithm very similar to the one pointed out in post #2. If both x and y are floats, x^y is computationally very expensive in time (it does take lots of time or cpu cycles).
As documented, bc ^ operator supports only integer power arguments. e(l(x)/3) however works. You can define it as a function if you like. Or use a somewhat more elaborated calculator.