Åk 6–9
 
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6.6 If the Exponent is 0 
What happens if the exponent is 0? 

In order to solve this problem, we need to use the power rules for division which can be found on page 6.5 Exponent Laws. The second exponent rule on that page looks like this:

ab

ac
= ab-c

Let’s put in a number instead of variables and use the exponent rules.

Example 1

What is
24

24
?

24

24
= 24-4 = 20 according the exponent rules.

24

24
can also be calculated like this:


24

24
=
2 · 2 · 2 · 2

2 · 2 · 2 · 2
= 16

16
= 1 by factorizing the powers.

So, it seems that:

20 = 1



Example 2

What is
32

32
?


32

32
= 32-2 = 30

32

32
can also be calculated like this:


32

32
=
3 · 3

3 · 3
=
9

9
= 1

So, it seems that:

30 = 1


With these two examples, we can accept the following definition of powers with the exponent 0.

For all numbers a (except = 0) it follows that: 

a0 = 1