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:

2^{2} = 2 × 2 = 4

4^{3} = 4 × 4 × 4 = 64

3^{4} = 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} = ^{y}n^{x}

Also, remember the following:

n^{1} = n

n^{0} = 1