Indicies

You can perform operations on numbers that have been squared cubed or raised to higher powers. There are three rules to remember for multiplying, dividing, and the power of a power.

Multiplying

When multiplying add the powers.

2³ × 2⁴ = (2 × 2 × 2) × (2 × 2 × 2 × 2)

= 2⁷

Dividing

When dividing subtract the powers.

2⁵ ÷ 2² =  = 2 × 2 × 2 (Cancelling two of the 2s)

= 2³

The power of a power

When taking the power of a number already raised to a power, multiply the powers.

For example this is how to find the square of 2³.

square of 2³ = (2³)² = (2 × 2 × 2) × (2 × 2 × 2) = 2⁶

Notice that the answer has an index of 6, which comes from multiplying the powers at the beginning (3 x 2). Here is another example.

(2²)⁴ = (2 × 2) × (2 × 2) x (2 × 2) × (2 × 2) = 2⁸

So you see that in both examples the powers have been multiplied (3x2 and 2x4)