Multiplication

How can we work out 2³ × 2⁵?

2³ = 2 × 2 × 2

2⁵ = 2 × 2 × 2 × 2 × 2

so 2³ × 2⁵ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁸

There are 3 twos from 2³ and 5 twos from 2⁵, so altogether there are 8 twos.

Examples

2⁵ × 2⁴ = 2^{(5 + 4)} = 2⁹

2⁷ × 2³ = 2^{(7 + 3)} = 2¹⁰

The rule also works for other numbers, so

3⁴ × 3² = 3^{(4 + 2)} = 3⁶

25⁶ × 25⁴ = 25^{(6 + 4)} = 25¹⁰

Division

If you divide 2⁵ by 2³ you see that some of the 2's cancel:

So 2⁵ ÷ 2³ = 2²

Example

2⁵ ÷ 2² = 2^{(5 - 2)} = 2³

2⁷ ÷ 2³ = 2^{(7 - 3)} = 2⁴

The rule also works for other numbers, so

5¹⁰ ÷ 5³ =5^{(10 - 3)} = 5⁷

45⁹ ÷ 45⁴ = 45^{(9 - 4)} = 45⁵