1. Laws of Indices or Powers © Christine Crisp

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

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

7. 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.

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

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

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

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

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

13. Laws of Indices Fractional Powers i.e. the  4

14. 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

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

16. 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.

17. 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.

18. Laws of Indices