Succeed with maths – Part 2
Succeed with maths – Part 2

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Succeed with maths – Part 2

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:

equation left hand side 10 super six divided by 10 squared equals right hand side 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 divided by 10 multiplication 10

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

10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 multiplication 10 divided by 10 multiplication 10 times equation sequence equals 10 multiplication 10 multiplication 10 multiplication 10 equals 10 super four

Therefore, equation left hand side 10 super six division 10 squared equals right hand side 10 super four

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:

equation sequence 10 super six division 10 squared equals 10 super open six minus two close equals 10 super four

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.

Activity 4 Dividing powers with the same base number

Timing: Allow approximately 5 minutes

Without using your calculator, work out each of the following:

  • a.four super seven division four super five

Answer

  • a.multiline equation line 1 equation sequence four super seven division four super five equals four super open seven minus five close equals four squared line 2 four squared equals 16

  • b.three super five division three super four

Answer

  • b.multiline equation line 1 equation sequence three super five division three super four equals three super open five minus four close equals three super one line 2 three super one equals three

  • c.two super four division two super negative two

Answer

  • c.multiline equation line 1 equation sequence two super four division two super minus two equals two super open four minus open minus two close close equals two super six line 2 equation sequence two super six equals two multiplication two multiplication two multiplication two multiplication two multiplication two equals 64

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.

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