Indices

a^m means a multiplied by itself

a^m means a multiplied by itself m times. Here, a is the base and m is the power, exponent, or index.

When powers have the same base

When powers have the same base, multiplication adds the indices: a^m × a^n = a^(m+n). The printed form in the chapter is a^m × a^m = a^(m+m), and exam

When powers have the same base

When powers have the same base, division subtracts the indices: a^m ÷ a^n = a^(m-n).

A power raised to another power

A power raised to another power means the indices are multiplied: (a^m)^n = a^(mn).

(a×b)^m = a^m × b^m

(a×b)^m = a^m × b^m and (a/b)^m = a^m / b^m.