2.4 Dividing powers

Now consider division in the same way. For example:

So 10³ ÷ 10² = 10¹ and 10⁶ ÷ 10² = 10⁴, which suggests that dividing the powers of ten means subtracting the powers. You can see that the two tens underneath have cancelled with two of the tens on top in each case, which shows why the number of tens underneath is subtracted from the number on top. This argument applies equally well to any number. For example:

Work out 7⁵ ÷ 7³ on your calculator to check this.