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

2. Laws of Indices Generalizing this, we get: Multiplying with Indices e.g.1 e.g.2

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

4. Laws of Indices Generalizing this, we get: Dividing with Indices Cancel e.g.

5. Laws of Indices Powers of Powers e.g.by rule (1)

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

7. Laws of Indices A Special Case e.g. Simplify Using rule (3) Also,

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

9. Laws of Indices Another Special Case e.g. Simplify Using rule (3) Also,

10. Laws of Indices e.g. Simplify Using rule (3) Also, So, Another Special Case

11. Laws of Indices Generalizing this, we get: e.g. 1 e.g. 2 Another Special Case

12. Laws of Indices 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 numbersand

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

14. Laws of Indices SUMMARY The following are the laws of indices:

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

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

17. Laws of Indices

18. 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.

19. Laws of Indices SUMMARY The following are the laws of indices:

20. Laws of Indices 1. 2. 3. Examples

21. Laws of Indices 4. 5. 6.