Computing powers of a number

Although most languages have a builtin pow function that computes powers of a number, you can write a similar function recursively, and it can be very efficient. The only hitch is that the exponent has to be an integer.

Suppose you want to compute $x^n$, where $x$ is any real number and $n$ is any integer. It's easy if $n$ is $0$, since $x^0 = 1$ no matter what $x$ is. That's a good base case.

So now let's see what happens when $n$ is positive. Let's start by recalling that when you multiply powers of $x$, you add the exponents: $x^a . \space x^b = x^{a + b}$ for any base $x$ ...