Indices — Formula Sheet

a^m = a multiplied by itself m times

a^0 = 1

a^n = 1 / a^-n

a^-n = 1 / a^n

a^(m/n) = nth root of a^m

Product Law: a^m × a^n = a^(m+n)

Quotient Law: a^m / a^n = a^(m-n)

Power Law: (a^m)^n = a^(mn)

(a × b)^m = a^m × b^m

27^-1/3 = 1/3

9^(3/2) - 3(5)^0 - (1/81)^(-1/2) = 15

If 1176 = 2^p · 3^q · 7^r, then p = 3, q = 1, r = 2

2^p · 3^q · 7^-r = 24/49

2^(2x+3) - 9 × 2^x + 1 = 0 gives x = -3 or x = 0

When powers have the same base, multiplication adds the indices: a^m × a^n = a^(m+n).

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

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

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