Here is a recursive algorithm to compute 32^n for a non-negative integer n:
1. If n = 0, return 1.
2. If n is even, recursively compute 32^(n/2) and square the result.
3. If n is odd, recursively compute 32^((n-1)/2), square the result, and multiply by 32.
The algorithm works by repeatedly dividing n by 2 and computing the result of 32 raised to that power. If n is even, we can compute 32^n by squaring 32^(n/2). If n is odd, we can compute 32^n by multiplying 32^((n-1)/2) by itself (i.e., squaring it) and then multiplying by 32. The base case is when n = 0, in which case we return 1 (since 32^0 = 1).