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3. Higher Mathematics Indices www.maths4scotland.co.uk Next

4. Indices Higher Mathematics What are Indices Indices are a mathematical shorthand If, we have: We can say that this is: 3 multiplied by itself 5 times We write this as: pronounced 3 to the power 5 3 is the BASE 5 is the POWER or INDEX

5. Indices Higher Mathematics What are Indices The plural of INDEX is is written in INDEX form also known as power form or power notation INDICES So,

6. Indices Higher Mathematics Rules of Indices

7. Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

8. Indices Higher Mathematics 3 times 4 times 7 times

9. Indices Higher Mathematics m times n times m + n times Generalising

10. Indices Higher Mathematics When multiplying We ADD the indices Generalising

11. Indices Higher Mathematics Examples Remember – to MULTIPLY you ADD the indices

12. Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

13. Indices Higher Mathematics 5 times 2 times 2 terms on the bottom will cancel out 2 terms on the top

14. Indices Higher Mathematics 5 times 2 times 5 - 2 terms 2 terms on the bottom will cancel out 2 terms on the top

15. Indices Higher Mathematics m times n times m - n terms n terms on the bottom will cancel out n terms on the top Generalising

16. Indices Higher Mathematics When dividing We SUBTRACT the indices Generalising

17. Indices Higher Mathematics Examples Remember – to DIVIDE you SUBTRACT the indices

18. Indices Higher Mathematics Rules of Indices Consider the following What can we make of it ? Can we generalise to make a rule ?

19. Indices Higher Mathematics 3 times 4 times 4  3 terms

20. Indices Higher Mathematics m times n times m  n terms

21. Indices Higher Mathematics Examples Remember – for POWERS you MULTIPLY the indices

22. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

23. Indices Higher Mathematics 3 times Recall division

24. Indices Higher Mathematics Examples Remember – anything to the power of 0 is 1

25. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

26. Indices Higher Mathematics 3 times 2 times Recall division

27. Indices Higher Mathematics Examples Remember – anything to the power of 1 is itself

28. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

29. Indices Higher Mathematics 3 times 4 times Recall division

30. Indices Higher Mathematics Rules of Indices a ‘minus’ index means ‘1 over’ A useful way of remembering this

31. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

32. Indices Higher Mathematics 2 times 5 times Recall division

33. Indices Higher Mathematics m times m +n times Generalising

34. Indices Higher Mathematics Examples Remember – minus means 1 over Express in positive index form

35. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

36. Indices Higher Mathematics Recall multiplication ButSo, Hence Thus

37. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

38. Indices Higher Mathematics Recall multiplication and, Hence Thus n times

39. Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form

40. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? What meaning can we give to

41. Indices Higher Mathematics Recall powers Thus So,But,

42. Indices Higher Mathematics Rules of Indices What can we make of it ? Can we deduce a meaning from what we know so far ? Finally, what meaning can we give to

43. Indices Higher Mathematics Examples Remember – fraction denominator gives the root Express in root form Remember – fraction numerator gives the power

44. Indices Higher Mathematics Recall Then and,

45. Indices Higher Mathematics Examples Express in root form Remember – minus means 1 over

46. Indices Higher Mathematics Rules of Indices Multiplying Dividing Powers

47. Indices Higher Mathematics Special Indices Power of 0 Power of 1

48. Indices Higher Mathematics Negative and Fractional Indices Negative Fraction Negative fraction minus means ‘1 over’

49. Indices Higher Mathematics More Examples - 1 Simplify

50. Indices Higher Mathematics More Examples - 2 Simplify

51. Indices Higher Mathematics More Examples - 3 Multiply out the brackets

52. Indices Higher Mathematics More Examples - 4 Simplify

53. Indices Higher Mathematics More Examples - 5 Solve the equation:

54. Indices Higher Mathematics More Examples - 6 Simplify and express in positive index form

55. Indices Higher Mathematics More Examples - 7 Write in root form

56. Indices Higher Mathematics More Examples - 8 Write in index form

57. Indices Higher Mathematics More Examples - 9 Evaluate

58. Indices Higher Mathematics More Examples - 10 Simplify

59. Indices Higher Mathematics More Examples - 11 Simplify

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