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.

2^{3} × 2^{4} = (2 × 2 × 2) × (2 × 2 × 2 × 2)

= 2^{7}

## Dividing

When dividing subtract the powers.

2^{5} ÷ 2^{2} = = 2 × 2 × 2 (Cancelling two of the 2s)

= 2^{3}

## 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 2^{3}.

square of 2^{3} = (2^{3})^{2} = (2 × 2 × 2) × (2 × 2 × 2) = 2^{6}

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.

(2^{2})^{4} = (2 × 2) × (2 × 2) x (2 × 2) × (2 × 2) = 2^{8}

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

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