A definition of exponentiation as an operation made from multiplication seem to be similar to a definition of multiplication made from addition.

I.e., 2*5 is 2 + 2 + 2 .. 2, for the total of five numbers two. Similarly, 2^5 is 2 * 2 * 2 .. 2, for the total of five numbers two.

Yet multiplication is commutative, but similarly defined exponentiation is not. Why?