I can calculate the result of $x^y$ provided that $y \in\mathbb{N}, x \neq 0$ using a simple recursive function:
$$ f(x,y) = \begin {cases} 1 & y = 0 \\ (x)f(x, y-1) & y > 0 \end {cases} $$
or, perhaps more simply stated, by multiplying $x$ by itself $y$ times.
Unfortunately, I am unsure how I can numerically approximate $x^y$ for non-integer rationals.
For example, what method can I use to approximate 33.3?
If possible, I would like to be able to do this using only elementary arithmetic operations, i.e. addition, subtraction, multiplication, and division.