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# NOTE MATH FORM 3 - INDICES

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### NOTE MATH FORM 3 - INDICES

1. 1. Friday, January 25, 2013 AIRIL AHMAD
2. 2. Friday, January 25, 2013 INDICES HJ. AIRIL AHMAD AIRIL AHMAD
3. 3. Friday, January 25, 2013 6 2 23= 2 x 2 x 2 8 4 3 2.5 x 2.5 x 2.5 7 5x5x5x5x5x5x5 AIRIL AHMAD
4. 4. Friday, January 25, 2013 Indices is read as 3 to the power 4 3 of 4 where 3 is the base and 4 is the index. AIRIL AHMAD
5. 5. Friday, January 25, 2013 Repeated Multiplication  63= 6 x 6 x 6  25= 2 x 2 x 2 x 2 x 2  (-g)4= (-g) x (-g) x (-g) x (-g)  (3y)3= (3y) x (3y) x (3y) AIRIL AHMAD
6. 6. Friday, January 25, 2013 Repeated Multiplication 9 x9x9= 25 x 25 x 25 x 25 x 25 =  (-kg) x (-kg) x (-kg) x (-kg)=  (6w) x (6w) x (6w) = AIRIL AHMAD
7. 7. Friday, January 25, 2013 By using the calculator find the values of the following indices 1. 65 = 6. (½)5 = 2. (-12)4 = 7. (-¼) 4 = 3. (2.4)4 = 8. (¾)4 = 4. 153 = 9. (²/3)3 = 5. (32.9)2 = 10. (50)4 = AIRIL AHMAD
8. 8. Friday, January 25, 2013 Expressing a certain number in the index notation. Example 1: Express 32  Example 2: Express 625 in in the index notation the index notation with with base 2. base 5. 2 32 5 625 2 16 5 125 2 8 5 25 2 2 4 2 1 2 5 5 5 1 5 4 AIRIL AHMAD
9. 9. Friday, January 25, 2013 Exercise Express each of the following in the index notation with the base given in the brackets 1. 16 (base 2) 6. 243 (base 3) 2. 81 (base 3) 7. 216 (base 6) 3. 64 (base 2) 8. 343 (base 7) 4. 125 (base 5) 9. 128 (base 2) 5. 256 (base 4) 10. 10 000 (base 10) AIRIL AHMAD
10. 10. Friday, January 25, 2013 MULTIPLICATION OF NUMBERS IN INDEX NOTATION HJ. AIRIL AHMAD AIRIL AHMAD
11. 11. Friday, January 25, 2013 Example:  1. 32 x 33 = 3 ×x 3 × 33 3 x 3× 3 × 3  3  x 3  x =35 5times  2. 93 x 94 = 9 × 9 × 9 × 9 × 9 × 9 × 9 =97 x x x x x x     7 times AIRIL AHMAD
12. 12. Friday, January 25, 2013 Example: 3. g 4 x g5 = g × g × g × g ×xgg×xgg×xgg×xgg xgg gxgxgxg × =g9   9 times 4. 1518 x 1514 = AIRIL AHMAD
13. 13. Friday, January 25, 2013 Verify a x a = a m n m+n 1. 5 x 5 = 4 5 54+5 = 59 2. h11 x h18 = h11+18 = h29 AIRIL AHMAD
14. 14. Friday, January 25, 2013 Exercise Pg 103 Ex.5.2A 1abcdef 2abc AIRIL AHMAD
15. 15. Friday, January 25, 2013 MULTIPLICATION OF NUMBERS OR ALGEBRAIC TERMS WITH THE SAME BASE HJ. AIRIL AHMAD AIRIL AHMAD
16. 16. Friday, January 25, 2013 Example:1. 3a2 x 2a = 3 (3x2) a2+3 =6a52. 6f5 x 2f3= (6x2) f5+3 =12f83. 4m2 x 2m9= (4x2) m2+9 =8m114. 8z9 x 3z3= (8x3) z9+3 =24z12 AIRIL AHMAD
17. 17. Friday, January 25, 2013 Exercise:1. 9d2 x 2d10= (9x2) d2+10 =18d122. 10n4 x 2n3= (10x2) n4+3 =20n73. 4w2 x w14= (4x1) w2+14 =4w164. z19 x 34z3= (1x34) z19+3 =34z22 AIRIL AHMAD
18. 18. Friday, January 25, 2013 Simplify multiplication of numbers or algebraic terms with different bases Example: 1. 32 x 23 x 34 x 27= 3 2+4 x 23+7 =36 x 210 2. k x m x k x m= 5 6 8 7 k 5+8 x m6+7 =k13 x m13 3. (½)9 x (½)4 x (¼)12 x (¼)9= AIRIL AHMAD
19. 19. Friday, January 25, 2013 Exercise Pg 104 Ex.5.2B 1-10 AIRIL AHMAD
20. 20. Friday, January 25, 2013 DIVISION OF NUMBERS IN INDEX NOTATION HJ. AIRIL AHMAD AIRIL AHMAD
21. 21. Friday, January 25, 2013 Verify a ÷ a = a m n m-n 1. 5 7 ÷ 5 = 5 57-5 = 52 2. h21 ÷ h18 = h21-18 = h3 AIRIL AHMAD
22. 22. Friday, January 25, 2013 Example: 1. 35 ÷ 33 = 2. k14 ÷ k5 = 3. 99 ÷ 94 = 4. 1518 ÷ 1514 = AIRIL AHMAD
23. 23. Friday, January 25, 2013 Exercise Pg 106 Ex.5.3A 1abcdef 2ab AIRIL AHMAD
24. 24. Friday, January 25, 2013 Exercise: 1. 9d ÷ 3d = 12 2 (9 ÷3) d12-2 =3d10 2. 10n4 ÷ 2n3= (10 ÷ 2) n4-3 =5n1 3. 40w27 ÷ 4w14= (40 ÷ 4) w27-14 =10w13 4. 25z19 ÷ 5z3= (25 ÷5) Z19-3 =5z16 AIRIL AHMAD
25. 25. Friday, January 25, 2013 Exercise Pg 106 Ex.5.3A 2cdefgh 3abcd AIRIL AHMAD
26. 26. Friday, January 25, 2013 RAISING NUMBERS AND ALGEBRAIC TERMS IN INDEX NOTATION AIRIL AHMAD AIRIL AHMAD
27. 27. Friday, January 25, 2013 Verify (a ) = a m n mn 1. (5 ) = 7 5 57x5 = 535 2. (h20)8 = h20x8 = h160 AIRIL AHMAD
28. 28. Friday, January 25, 2013 3. (2c ) = 7 5 2 1x5 c7x5 = 25c35 4. (32h8)8 = 3 2x8 h8x8 = 316h64 AIRIL AHMAD
29. 29. Friday, January 25, 2013 Exercise Pg 108 Ex.5.4A 1-8 AIRIL AHMAD
30. 30. Friday, January 25, 2013 Exercise Pg 109 Ex.5.4B Question 1 only AIRIL AHMAD
31. 31. Friday, January 25, 2013 AIRIL AHMAD
32. 32. Friday, January 25, 2013 COMPUTATIONS INVOLVING NEGATIVE INDICES HJ. AIRIL AHMAD AIRIL AHMAD
33. 33. Friday, January 25, 2013 1 Verify a = -n an 1. 1 8 = -7 7 8 2. f -2 = 1 2 f AIRIL AHMAD
34. 34. Friday, January 25, 2013 Exercise Pg 112 Ex.5.5A 1 AND 2 AIRIL AHMAD
35. 35. Friday, January 25, 2013PERFORM COMPUTATIONSINVOLVING NEGATIVE INDICES Example: 1. 2-2 x 2-4 = 2-2+ (-4) = 2-2-4 = 2-6 2. 7-5 ÷ 7-2 = 7-5 - (-2) = 7-5+2 = 7-3 3. (8-2)-4 = 8-2 x (-4) = 88 AIRIL AHMAD
36. 36. Friday, January 25, 2013 E xercise Pg 113 Ex.5.5B Question 1-8 AIRIL AHMAD
37. 37. Friday, January 25, 2013 AIRIL AHMAD
38. 38. Friday, January 25, 2013 COMPUTATIONS INVOLVING FRACTION INDICES HJ. AIRIL AHMAD AIRIL AHMAD
39. 39. Friday, January 25, 2013 ( a) m m n Verify a = n m power a n root AIRIL AHMAD
40. 40. Friday, January 25, 2013 ( a) m m n Verify a = n 1. 8 = ¼ ( 8) 4 1 2. f ¾ = ( f) 4 3 AIRIL AHMAD
41. 41. Friday, January 25, 2013 Change to root notation: 1. 1 2. 1 25 = 2 27 = 3 3. 1 4. 1 32 = 5 49 = 2 AIRIL AHMAD
42. 42. Friday, January 25, 2013 Calculate the values using calculator: ( 81) 1.Press √¯¯ 1. 1 1 81 = 2.Press 81 2 2 3.Press = 4.Press ^ =9 5.Press 1 6.Press = AIRIL AHMAD
43. 43. Friday, January 25, 2013 1.Press 4 ( 81) 2. 1 2.Press shift ^ 1 81 = 4 4 3.Press 81 4.Press = 5.Press ^ =3 6.Press 1 7.Press = AIRIL AHMAD
44. 44. Friday, January 25, 2013 Example: Calculate the values: 1. 1 2. 1 25 2 27 3 3. 1 4. 1 32 5 49 2 AIRIL AHMAD
45. 45. Friday, January 25, 2013 Exercise Pg 118 Ex.5.6D 1 - 10 AIRIL AHMAD
46. 46. Friday, January 25, 2013 Exercise Pg 117 Ex.5.6C 1 2 3 5 6 7 8 AIRIL AHMAD
47. 47. Friday, January 25, 2013 Exercise Pg 117 Ex.5.6C 1 - 8 AIRIL AHMAD

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