2.2 Dividing powers with the same base number

The rule for multiplying powers with the same base number is to add together the powers of these numbers. Let’s now consider what happens with division using the example of 10⁶ ÷ 10².

As you may already know, any division can be rewritten as a fraction and then simplified if appropriate. (Again Succeed with maths – Part 1. [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] looks at this topic.)

. This means that 10⁶ ÷ 10² can be shown as:

To simplify this both the top and bottom of the fraction can be divided by 10 and then by 10 again, giving:

Therefore,

If you look at the powers in this sum and the answer, you may notice that you can get the same result by subtracting the powers, giving:

This rule works with any power where the base numbers (in this case 10) are the same.

As with any new idea in maths the best way to cement these is to have a go at some examples. So see how you get on with the next activity on dividing numbers with the same base number.

Now you have two rules giving you a short cut when faced with calculations involving powers of the same base number. These can be summarised as follows:

• When multiplying powers with the same base number, add the powers.
• When dividing powers with the same base number, subtract the powers.

All the powers that have been dealt with so far were positive whole numbers and shortly you’ll look at negative powers. This leaves the number separating the positive and negative numbers, zero. Can a number actually be raised to the power of zero and if so, what does that mean? Let’s see in the next short section.