1. Unit 5 : Indices and Surds

2. Index, exponential, power
5.1 Principle of Indices
Index, exponential, power
Base

3. Indices Rule 1

4. Indices Rule 2

5. Indices Rule 3
From Rule 1

6. Indices Rule 4

7. Indices Rule 5

8. Indices Rule 6, 7 1

9. Indices Rule 8

10. Irrational Number
Number that cannot be expressed as a fraction of two integers

11. x x x Think! Which of the following is NOT a irrational number?

12. Surd Rules We can use the above rules to:
simplify two or more surds or
combining them into one single surd

13. Simplify the following surds :
Example 1:
Simplify the following surds :
Solution:

14. Simplify the following surds
Example 2:
Simplify the following surds
Solution:

15. Example 3:
Simplify the following surds
Solution: x

16. Simplify the following surds
Example 4:
Simplify the following surds
Solution: 3 49

17. Simplify the following surds
Example 5:
Simplify the following surds
Solution:

18. Simplify the following surds
Example 6:
Simplify the following surds
Solution:

19. Simplify the following surds
Example 7:
Simplify the following surds
Solution:

20. Simplify the following surds
Example 8:
Simplify the following surds
Solution:

21. 5.2 Rationalization of the Denominator
Process of removing a surd from the denominator
Example 9:
Solution:
Multiple together!

22. Objective is to remove surds from denominator
Example 10:
Solution:
Note!
Multiple together!
Objective is to remove surds from denominator
Conjugate Surds

23. Re-look into the question:
Example 11 :
Re-look into the question:
Multiply conjugate surds
Multiply denominator and numerator

24. Rationalize the denominators:
Example 12:
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and numerator

25. Rationalize the denominators:
Example 13:
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and numerator

26. Rationalize the denominators:
Example 14:
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and numerator

27. Rationalize the denominators:
Example 15:
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and numerator

28. Rationalize the denominators:
Example 16:
Rationalize the denominators:
Multiply conjugate surds
Multiply denominator and numerator

29. Multiply denominator and numerator
Example 17:
Rationalize the denominators:
Determine the LCM
Multiply denominator and numerator

30. Expand the denominators
Example 18:
Rationalize the denominators:
Expand the denominators
Find the LCM

31. Rationalize the denominators:
Example 19:
Rationalize the denominators:
Same denominator
Rationalization

32. Given that k = , evaluate
Example 20:

33. Change to common power Change to common base 5.3 Simplifying Indices
Think of how to make
it common power
Break each term into
its prime factor
Simplify the indices
within each term
Ensure that
common power
Combine the base
and simplify
Simplify the indices
across other terms

34. Change to common base Example 21: Plan Break each term into
its prime factor
Simplify the indices
within each term
Simplify the indices
across other terms

35. Change to common base Example 22: Break each term into
its prime factor
Simplify the indices
within each term
Simplify the indices
across other terms

36. Simplify the following:
Example 23:
Simplify the following:
Break each term into
its prime factor
Simplify the indices
within each term
Simplify the indices
across other terms

37. Example 24:
Simplify the following :

38. Evaluate the following:
Example 25:
Evaluate the following:
Think of how to make
it common power 3
Ensure that
common power
Combine the base
and simplify

39. Example 26:

40. Example 27: Simplify the indices within each bracket
using indices law
Multiply inner power
with other power

41. Surd Form as Question is
Example 28:
Simplify the indices
within each term
Simplify the indices
using indices law
Express the answer in
Surd Form as Question is
given in surd form

42. Surd Form as Question is
Example 29:
Simplify the indices
within each term
Simplify the indices
using indices law
Express the answer in
Surd Form as Question is
given in surd form

43. (a) Example 30: Express base into its prime factors Simplify the base
Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

44. (d) Example 31: Express base into its prime factors Simplify the base
Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

45. (f) Example 32: Express base into its prime factors Simplify the base
Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

46. (a) Example 33: Express base into its Desired power Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

47. Example 34:

48. Example 35: Express base into its Desired power Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

49. Example 36: Express base into its Desired power Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!

50. Example 37: Why? Express base into its Desired power Replace the term
with y
Simplify in terms of
y only.
No x term should
be seen!