note math form 3 - indices
TRANSCRIPT
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AIRIL AHMAD
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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Wednesday, April 12, 2023
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
HJ. AIRIL AHMAD
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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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Wednesday, April 12, 2023
MULTIPLICATION OF NUMBERS OR
ALGEBRAIC TERMS WITH THE SAME BASE
HJ. AIRIL AHMAD
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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
ExercisePg 106Ex.5.3A2cdefgh3abcd
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RAISING NUMBERS AND ALGEBRAIC TERMS IN INDEX
NOTATION
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Wednesday, April 12, 2023
Verify (am)n = amn
1. (57)5 = 57x5 = 535
2. (h20)8 = h20x8 = h160
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Wednesday, April 12, 2023
3. (2c7)5 = c7x5 = 25c35
4. (32h8)8 = h8x8 = 316h64
21x5
32x8
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Wednesday, April 12, 2023
ExercisePg 108Ex.5.4A1-8
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Wednesday, April 12, 2023
ExercisePg 109Ex.5.4BQuestion 1
only
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Wednesday, April 12, 2023
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COMPUTATIONS INVOLVING
NEGATIVE INDICES
HJ. AIRIL AHMAD
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Wednesday, April 12, 2023
Verify a-n =
1. 8-7 = 78
1
2. f-2 = 2
1
f
na
1
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Wednesday, April 12, 2023
ExercisePg 112Ex.5.5A1 AND 2
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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
Verify a = mn an
m
n
m
apower
root
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Wednesday, April 12, 2023
Verify a =
1. 8¼ = 82. f ¾ =
mn a
f
n
m
41
43
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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
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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Wednesday, April 12, 2023
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