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Maths

Powers and roots - Foundation

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Rules of indices

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 x 2 x 2 x 2 x 2 over 2 x 2 = 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)

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