Divide and Conquer: Exponentiation
Consider exponentiation, in which some number x is raised to some non-negative integer power n. If x is 3 and n is 20, then xn is
320 = 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3 ⋅ 3
There are 19 multiplications in all.
Multiplication is associative, so we can perform those multiplications in any order we please.