1. “Teach A Level Maths” Vol. 1: AS Core Modules
19: Laws of Indices
© Christine Crisp

2. Module C1 Module C2 Edexcel AQA MEI/OCR OCR
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3. Multiplying with Indices
e.g.1
e.g.2
Generalizing this, we get:

4. Multiplying with Indices
If m and n are not integers, a must be positive
e.g.3

5. Dividing with Indices
e.g.
Cancel
Generalizing this, we get:

6. Powers of Powers
e.g.
by rule (1)

7. Exercises
Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

8. A Special Case
e.g. Simplify
Using rule (3)
Also,

9. A Special Case
e.g. Simplify
Using rule (2)
Also,
So,
Generalizing this, we get:

10. Another Special Case
e.g. Simplify
Using rule (3)
Also,

11. Another Special Case
e.g. Simplify
Using rule (3)
Also,
So,

12. Another Special Case
Generalizing this, we get:
e.g. 1
e.g. 2

13. Rational Numbers
A rational number is one that can be written as
where p and q are integers and
e.g.
and
are rational numbers
are not rational numbers
and

14. p is the power Rational Numbers
The definition of a rational index is that
e.g.1
p is the power
q is the root
e.g.2
e.g.3

15. SUMMARY
The following are the laws of indices:

16. Exercises
Without using a calculator, use the laws of indices to express each of the following as an integer 1. 2. 3.

17. Exercises
Without using a calculator, use the laws of indices to express each of the following as an integer or fraction 4. 5. 6.

19. The following slides contain repeats of information on earlier slides, shown without colour, so that they can be printed and photocopied.
For most purposes the slides can be printed as “Handouts” with up to 6 slides per sheet.

20. SUMMARY
The following are the laws of indices:

21. 1. 2. 3.
Examples

22. 4. 5. 6.