Why Learn Exponents?

Exponents show up everywhere in algorithms. Time complexity: $O(n^2)$, $O(2^n)$. Space complexity: $O(\log n)$. Bit manipulation: $2^k$ subsets.

If you can't compute $2^{20}$ or compare $n^2$ vs $2^n$, you'll struggle to choose the right algorithm. A $2^n$ solution works for $n \leq 20$, but fails at $n = 30$.

Now let me show you a real problem where you need exponentiation. This is your entry problem: computing $x^n$ efficiently.