Given an integer base x and a non-negative integer exponent n, compute x raised to the power n. Multiplying x by itself n times works, but it treats every exponent as fundamentally n separate units of work. Recursive squaring exploits a shortcut instead: x^n is just (x^(n/2))² when n is even (with one extra factor of x tacked on when n is odd) — so the exponent can be halved at every single recursive call rather than merely decremented. Reaching the base case (n=0, trivially 1) this way takes only O(log n) calls, turning what would be a million multiplications for a million-sized exponent into roughly twenty.