1. Friday, January 25, 2013
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2. Friday, January 25, 2013
INDICES
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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
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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.
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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)
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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) =
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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 =
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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
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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)
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10. Friday, January 25, 2013
MULTIPLICATION
OF NUMBERS IN
INDEX NOTATION
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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
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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 =
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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
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14. Friday, January 25, 2013
Exercise
Pg 103
Ex.5.2A
1abcdef
2abc
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15. Friday, January 25, 2013
MULTIPLICATION OF
NUMBERS OR
ALGEBRAIC TERMS
WITH THE SAME BASE
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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
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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
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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=
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19. Friday, January 25, 2013
Exercise
Pg 104
Ex.5.2B
1-10
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20. Friday, January 25, 2013
DIVISION OF
NUMBERS IN INDEX
NOTATION
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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
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22. Friday, January 25, 2013
Example:
1. 35 ÷ 33 =
2. k14 ÷ k5 =
3. 99 ÷ 94 =
4. 1518 ÷ 1514 =
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23. Friday, January 25, 2013
Exercise
Pg 106
Ex.5.3A
1abcdef
2ab
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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
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25. Friday, January 25, 2013
Exercise
Pg 106
Ex.5.3A
2cdefgh
3abcd
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26. Friday, January 25, 2013
RAISING NUMBERS
AND ALGEBRAIC
TERMS IN INDEX
NOTATION
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27. Friday, January 25, 2013
Verify (a ) = a m n mn
1. (5 ) =
7 5 57x5 = 535
2. (h20)8 = h20x8 = h160
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28. Friday, January 25, 2013
3. (2c ) = 7 5
2 1x5 c7x5 = 25c35
4. (32h8)8 = 3
2x8 h8x8 = 316h64
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29. Friday, January 25, 2013
Exercise
Pg 108
Ex.5.4A
1-8
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30. Friday, January 25, 2013
Exercise
Pg 109
Ex.5.4B
Question 1
only
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31. Friday, January 25, 2013
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32. Friday, January 25, 2013
COMPUTATIONS
INVOLVING
NEGATIVE INDICES
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33. Friday, January 25, 2013
1
Verify a = -n
an
1. 1
8 = -7
7
8
2. f -2
=
1
2
f
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34. Friday, January 25, 2013
Exercise
Pg 112
Ex.5.5A
1 AND 2
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35. Friday, January 25, 2013
PERFORM COMPUTATIONS
INVOLVING 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
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36. Friday, January 25, 2013
E xercise
Pg 113
Ex.5.5B
Question
1-8
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37. Friday, January 25, 2013
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38. Friday, January 25, 2013
COMPUTATIONS
INVOLVING
FRACTION INDICES
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39. Friday, January 25, 2013
( a)
m
m
n
Verify a = n
m power
a n root
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40. Friday, January 25, 2013
( a)
m
m
n
Verify a = n
1. 8 = ¼
( 8)
4
1
2. f ¾
=
( f)
4
3
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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
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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 =
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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 =
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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
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45. Friday, January 25, 2013
Exercise
Pg 118
Ex.5.6D
1 - 10
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46. Friday, January 25, 2013
Exercise
Pg 117
Ex.5.6C
1 2 3 5 6 7 8
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47. Friday, January 25, 2013
Exercise
Pg 117
Ex.5.6C
1 - 8
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