���˿���

Indices are a way of writing numbers in a more convenient form. The index or power is the small, raised number next to a normal letter or number. It represents the number of times that normal letter or number has been multiplied by itself, for example:

a² = a × a

6⁴ = 6 × 6 × 6 × 6

b⁵ = b × b × b × b × b

For b⁵, b is the ‘base number’ and 5 is the ‘index’.

Multiplying indices

To multiply indices, add the powers together.

Example

2⁴ × 2² = (2 × 2 × 2 × 2) × (2 × 2)

= 2 × 2 × 2 × 2 × 2 × 2

= 2⁶

Dividing indices

To divide indices, subtract the powers.

Example

Raising a power to a power

When a power is raised to a power, multiply the powers

Example

(5³)² = 5³ × 5³.

= 5⁶, using the condition for multiplying indices

Whole numbers and indices

We need to deal with the numbers and the powers separately. First multiply the numbers in front of the letters together, and then use the rule for multiplying indices to deal with the letters and powers.

Example

2a³ × 3a⁴

2 × 3 = 6

a³ × a⁴ = a⁷

So, 2a³ × 3a⁴ = 6a⁷