Power - Implementation (The code)

Here's the recursive solution:

function power(x, n)
    if n = 0 then
        return 1
    if n < 0 then
        x := 1 / x
        n := -n
    if n is even then
        half := power(x, n / 2)
        return half * half
    else
        return x * power(x, n - 1)

The base case is $n = 0$, which returns $1$. For negative $n$, you flip $x$ to $1/x$ and make $n$ positive. Then you halve $n$ at each recursive step, giving $O(\log n)$ time and $O(\log n)$ space for the call stack.