chapter 1 exponents (laws of exponents)
TRANSCRIPT
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
What should students be able to do within this interactive?
1.
2.
with variable or numeric bases
1. For the Product of Powers: am x an = am + n
1.1 Multiplying the exponents
1.2 Multiplying or adding the bases
2. For the Quotient of Powers: am ÷ an = am - n
2.1 Dividing the exponents
2.2 Dividing the bases
2.3 Subtraction errors with negative exponents
3. For the Power of a Power: (am )n = amn
3.1 Multiplying the outer exponent onto both the base and the inner exponent.
3.2 Adding the exponents
3.3 Multiplication errors with negative exponents.
4. For the Product of a Power: (a x b)m = ambm
4.1 Not multiplying the outer exponent onto all of the inner exponents.
4.2 Adding the exponents
5. For the Quotient of a Power:
5.1 Not multiplying the outer exponent onto exponents of both the numerator and denominator.
5.2 Multiplication errors
5.3 Dividing exponents
5.4 Multiplying the exponent and the base together.
Chapter 1Exponents (Laws of Exponents)
Students should be able to understand and use of the laws of exponents.
Students should be able to simplify expressions that have positive, negative, or zero exponents
Common Mistakes Made within Each Law
𝒙
𝒚
𝒏
=𝒙𝒏
𝒚𝒏
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
6. For the Zero Exponents: a0 = 1 and x ≠ 0 6.1 Thinking the result of a zero exponent is zero.
6.2 Thinking the result of a zero exponent is the value of the base.
6.3 Not understanding the meaning of a zero exponent and where it could arise in a question.
6.4 Not understanding why the result of a zero exponent is always one.
7. For the For Negative Exponents: and x ≠ 0
7.1 Thinking that all negative exponents result in negative answers.
7.2 Not making the numerator 1 when reciprocating the base.
7.3 Not understanding the meaning of a negative exponent.
7.4 Forgetting to make the exponent positive after it has been reciprocated.
7.5 Not distinguishing between a negative base and negative exponent.
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𝒙−𝒏 =𝟏
𝒙𝒏
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
2. Complete all the missing parts in the following table:
(d6 x d-4) x (d3 x d8) =
(22m5) x (2m9) =
(5w8) x (7w2) =
m4 x m9 =
16 x 25 x 26 =
125 x 5-5 x 52 =
Laws of Exponents
1. Complete all the missing parts in the following table:
m10 x m2 x m3 =
63 x 62 =
Practice 1
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
What should students be able to do within this interactive?
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What should students be able to do within this interactive?
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Practice 2Laws of Exponents
Home Work.....
𝑥10𝑦3
𝑥2𝑦
𝑎2𝑏8𝑐5
𝑎𝑏3𝑐2
𝑥18𝑦9
𝑥6𝑦6
𝑎5
𝑏8×𝑏9
𝑎2×𝑎𝑏4
𝑏
12𝑎8𝑏17
4𝑎10𝑏6×27𝑎𝑏7
9𝑎2𝑏
𝑥3𝑛−2𝑦2𝑛−1
𝑥𝑛𝑦
25𝑎𝑏5
−5𝑎−10𝑏−8
−54𝑎14𝑏9
−6𝑎−2𝑏7
𝑥5(𝑦 + 𝑧)13
𝑥2(𝑦 + 𝑧)8
𝑎−2𝑏
𝑎3𝑏−4÷
𝑎𝑏−1
𝑎−3𝑏−4
−18𝑐9𝑑20
12𝑐10𝑑6
16𝑎8𝑏4
2𝑎3𝑏÷
𝑎2𝑏3𝑐
36𝑎4𝑏𝑐5
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
What should students be able to do within this interactive?
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What should students be able to do within this interactive?
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Practice 3
Laws of Exponents
Home Work.....
𝑎−2𝑏𝑎3𝑏−4
÷𝑎𝑏−1
𝑎−3𝑏−4
−18𝑐9𝑑20
12𝑐10𝑑6
16𝑎8𝑏4
2𝑎3𝑏 ÷𝑎2𝑏3𝑐36𝑎4𝑏𝑐5ษึ
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1. =
2. =
3. =
4. =
5. =
6. =
7. =
8. =
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
Practice 4Laws of Exponents
Complete all the missing parts in the following table:
𝑎5 ÷ 𝑎3
(𝑎−2)3
(𝑎−2𝑏)−4×(𝑎𝑏)4
(2−2𝑎4𝑏)−1× (4−2𝑏−5)
(23× 34)3
(22× 32)5
(12𝑎2𝑏𝑐)2
(10𝑎𝑏3)2
(23× 34)3
(22× 32)5
4𝑎𝑏𝑐
−6𝑥𝑦3×
−8𝑥2𝑦
12𝑎2𝑏𝑐2
−5𝑎2𝑏
7𝑐𝑑2÷10𝑎3𝑏2
21𝑐2𝑑
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1. =
2. =
3. =
4. =
5. =
6. =
7. =
8. =
Home Work.....
Complete all the missing parts in the following table:
𝑎8 ÷ 𝑎−4
(𝑎4)−6
(𝑎−5𝑏)−6×(𝑎𝑏)3
(2−5𝑎3𝑏)−7× (4−8𝑏−3)
(34× 5−2)2
(3−6× 54)3
(15𝑎4𝑏𝑐)−1
(10𝑎𝑏2)3
12𝑎𝑏𝑐
−2𝑥𝑦−2×
−6𝑥4𝑦
4𝑎5𝑏𝑐−3
−625𝑎3𝑏
81𝑐𝑑3÷125𝑎4𝑏−2
27𝑐−4𝑑
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1)
2)
1)
2)
0.00001452 0.00000000035468
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2.354 x 108 12.36 x 10-5
Express each of the following as an integer or a decimal.
1.325 x 106 4.4 x 10-3
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0.000048 0.00000000021
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0.000038
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0.000000000000299
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69,100,000
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149,600,000
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Express each of the following numbers in scientific notation.
600,000,0005,300,000
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149,600,000
0.000038
Example
Practice
Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
Practice 5Sciencetific Notation
Express each of the following numbers in scientific notation.
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1)
2)
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9.6 x 103 0.00456 x 10-7
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0.000007 0.00478
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15,234,000 94,251,000
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12,100,000 110,000,000
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0.5 x 109 7,000 x 103
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0.00023 0.0000000094
Express each of the following as an integer or a decimal.
1.325 x 106 4.4 x 10-3
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0.000048 0.00000000021
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85,300 52,700,000
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Express each of the following numbers in scientific notation.
5,300,000 600,000,000
Homework
Sciencetific Notation
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1)
2)
1)
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(2.34 x 105) x (7.12 x 10-4) (13.4 x 104) ÷ (4 x 105)
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(1.14 x 105) + (4.56 x 104) [(2.37 x 10-3) + (3.25 x 10-4)] ÷ (4.1 x 105)
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(4.5 x 10-3) ÷ (9 x 10-1)
Practice
Express each of the following numbers in scientific notation.
(4.2 x 10-4) x (2.6 x 102) (3.5 x 10-5) ÷ (1.4 x 108)
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Name: ................................................................... No: ..................... Class: M. 2/........ Date: .........................
Practice 6Apply Sciencetific Notation
Express each of the following numbers in scientific notation.
Example
(7.2 x 103) x (2 x 1015) = ....................................................................................................................................................
Topic: Exponent and Applying
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
1)
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(2.4 x 10-10) ÷ [(7.2 x 10-6) - (3.5 x 10-8)] [(4.37 x 10-4) + (2.16 x 10-5)] ÷ (3 x 10-3)
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(2.34 x 105) x (7.12 x 10-4) (13.4 x 104) ÷ (4 x 105)
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(6.4 x 106) x (5.1 x 10-3) (2.17 x 10-5) ÷ (7 x 104)
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(3.17 x 104) + (2.26 x 105) [(8.43 x 107) + (6.8 x 108)] ÷ (1.01 x 104)3
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(2 x 105) - (0.12 x 107)(32.6 x 102) x (42.56 x 103)
Express each of the following numbers in scientific notation.
(2.54 x 103) + (3.11 x 104) (6 x 105) - (3.1 x 103)
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Homework
Sciencetific Notation
Law of Indices
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
Score: 50 marks
1.
1.2)
1.5) (253m7) x (1252m-3)
2.
2.2) 125,040
2.3) 365,200,000,000
2.4) 0.000000465001
2.5) 0.000000000057306
3.
4.
5.
Express each of the following numbers in scientific notation. (20 Marks)
Express each of the following numbers in scientific notation. (5 Marks)
Express each of the following as an integer or a decimal. (5 Marks)
2.1) 4,832,000
3.1) 0.02407 x 107
3.2) 12.4 x 103
3.3) 3.05 x 106
3.4) 5.4 x 10-5
3.1) 0.305 x 10-5
4.1) (2.54 x 103) + (3.11 x 104)
4.4) [(3 x 106) - (0.6 x 107)] x (3 x 102)3
4.2) (3.75 x 104) ÷ (5 x 105)3
4.3) (12.5 x 10-3) x (3 x 10-6)
4.5) (2.5 x 10-8)2 ÷ [(2 x 10-5) + (30 x 10-6)]
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What are the 7 laws of exponents? List all of these. ( Bonus Point, 5 marks)+ 25
Complete all the missing parts in the following table. (15 marks)
1.1)
1.3)
1.4)
Name: .............................................................................. No: ................. Class: M. 2/1 Date: 07-June-2021
Post-test Chapter 1
Law of Indices
Directions: This exam includes 1 parts (ให้นักเรียนเขียนแสดงวิธีท ำอย่ำงละเอียด)
Time: 08.40 - 10.10 ( 90 minutes)
---------------------------------------------------------- Question ----------------------------------------------------------------------
(2−8× 35)7
(24× 33)5
−56a−2b
9cd−3÷7a3b3
36c4d
−27𝑐−8𝑑−21
34𝑐−30𝑑−4
𝑥−4(𝑎 + 𝑏)−8
𝑥−2(𝑎 + 𝑏)15
Law of Indices
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
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Law of Indices
Teacher: Sunisa Pengmanee
Mathematics 3 (Mathayom 2)..........
English Program 2021..........
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