Power Function - Problem Statement

Given a number $x$ and a non-negative integer $n$, compute $x^n$. For example, $2^{10} = 1024$ and $3^4 = 81$. You could multiply $x$ by itself $n$ times. That takes $n$ multiplications.

But there is a recursive approach that uses far fewer operations. Notice that $x^{10} = (x^5)^2$. Can you see what $x^{10}$ and $x^5$ have in common? Squaring $x^{n/2}$ halves the remaining exponent each step, so the answer arrives in $O(\log n)$ multiplications.