NOTE MATH FORM 3 - INDICES

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Wednesday, April 12, 2023

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INDICES

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23= 2 x 2 x 2

2.5 x 2.5 x 2.534

62

5 x 5 x 5 x 5 x 5 x 5 x 5

87

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Indices is read as 3 to the power

of 4 where 3 is the base

and 4 is the index.

43

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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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Repeated Multiplication

9 x 9 x 9 =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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By using the calculator find the values of the following indices

1. 65 =

2. (-12)4 =

3. (2.4)4 =

4. 153 =

5. (32.9)2 =

6. (½)5 =

7. (-¼) 4 =

8. (¾)4 =

9. (²/3)3 =

10. (50)4 =

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Expressing a certain number in the index notation.

Example 1: Express 32 in the index notation with base 2.

2 322 162 82 42 2 1

25

Example 2: Express 625 in the index notation with base 5.

5 6255 1255 255 5 1 54

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Exercise Express each of the following in the index notation

with the base given in the brackets

1. 16 (base 2)

2. 81 (base 3)

3. 64 (base 2)

4. 125 (base 5)

5. 256 (base 4)

6. 243 (base 3)

7. 216 (base 6)

8. 343 (base 7)

9. 128 (base 2)

10. 10 000 (base 10)

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MULTIPLICATION OF NUMBERS IN

INDEX NOTATION

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Example:

1. 32 x 33 = 3 x 3 x 3 x 3 x 3 =35 times5

33333

2. 93 x 94 = 9 x 9 x 9 x 9 x 9 x 9 x 9 =97 times7

9999999

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Example: 3. g4 x g5 = g x g x g x g x g x g x g x g x g =g9

times

ggggggggg9

4. 1518 x 1514 =

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Verify am x an = am+n

1. 54 x 55 = 54+5 = 59

2. h11 x h18 = h11+18 = h29

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ExercisePg 103Ex.5.2A1abcdef2abc

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MULTIPLICATION OF NUMBERS OR

ALGEBRAIC TERMS WITH THE SAME BASE

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Example:1. 3a2 x 2a3= (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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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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Simplify multiplication of numbers or algebraic terms with different bases

Example: 1. 32 x 23 x 34 x 27= 3 2+4 =36 x 210x 23+7

2. k5 x m6 x k8 x m7=

3. (½)9 x (½)4 x (¼)12 x (¼)9=

k 5+8 =k13 x m13x m6+7

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ExercisePg 104Ex.5.2B1-10

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DIVISION OF NUMBERS IN INDEX

NOTATION

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Verify am ÷ an = am-n

1. 57 ÷ 55 = 57-5 = 52

2. h21 ÷ h18 = h21-18 = h3

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Example:

1. 35 ÷ 33 =

3. 99 ÷ 94 =

2. k14 ÷ k5 =

4. 1518 ÷ 1514 =

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ExercisePg 106Ex.5.3A1abcdef2ab

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Exercise:1. 9d12 ÷ 3d2= (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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ExercisePg 106Ex.5.3A2cdefgh3abcd

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RAISING NUMBERS AND ALGEBRAIC TERMS IN INDEX

NOTATION

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Verify (am)n = amn

1. (57)5 = 57x5 = 535

2. (h20)8 = h20x8 = h160

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3. (2c7)5 = c7x5 = 25c35

4. (32h8)8 = h8x8 = 316h64

21x5

32x8

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ExercisePg 108Ex.5.4A1-8

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ExercisePg 109Ex.5.4BQuestion 1

only

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COMPUTATIONS INVOLVING

NEGATIVE INDICES

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Verify a-n =

1. 8-7 = 78

1

2. f-2 = 2

1

f

na

1

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ExercisePg 112Ex.5.5A1 AND 2

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PERFORM COMPUTATIONS INVOLVING NEGATIVE INDICESExample:

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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E xercisePg 113Ex.5.5BQuestion

1 - 8

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COMPUTATIONS INVOLVING

FRACTION INDICES

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Verify a = mn an

m

n

m

apower

root

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Verify a =

1. 8¼ = 82. f ¾ =

mn a

f

n

m

41

43

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Change to root notation:

2

1

25 31

27

5

1

32 2

1

49

1.

4.

2.

3.

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Calculate the values using calculator:

2

1

811. 12 81

1.Press √¯¯

2.Press 81

3.Press =

4.Press ^

5.Press 1

6.Press =

= 9

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4

1

812. 14 81

= 3

1.Press 4

2.Press shift ^

3.Press 81

4.Press =

5.Press ^

6.Press 1

7.Press =

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Example: Calculate the values:

2

1

25 3

1

27

5

1

32 2

1

49

1.

4.

2.

3.

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ExercisePg 118Ex.5.6D1 - 10

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ExercisePg 117Ex.5.6C1 2 3 5 6 7 8

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ExercisePg 117Ex.5.6C1 - 8

NOTE MATH FORM 3 - INDICES

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