An index is the number which is at the top right hand corner of a figure which denotes a power. The power of a number is how many times the number is multiplied by itself. For example:

2² = 2 × 2 = 4
4³ = 4 × 4 × 4 = 64
3⁴ = 3 × 3 × 3 × 3 = 81

When using indices you should remember the following things:

Multiplying adds the powers:

• n^x × n^y = n^x+y

Division subtracts the powers:

• n^x ÷ n^y = n^x-y

A negative index means the number is reciprocated:
n^-x = 1/n^x

For fractional indices, the numerator is the power of the base number and the denominator is the root of this number:
n^x/y = ^yn^x

Also, remember the following:
n¹ = n
n⁰ = 1