chapter 1 exponents (laws of exponents)

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?

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

=𝒙𝒏

𝒚𝒏

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.

*****************************************************************************************************

𝒙−𝒏 =𝟏

𝒙𝒏

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

Practice 2Laws of Exponents

Home Work.....

𝑥10𝑦3

𝑥2𝑦

𝑎2𝑏8𝑐5

𝑎𝑏3𝑐2

𝑥18𝑦9

𝑥6𝑦6

𝑏8×𝑏9

𝑎2×𝑎𝑏4

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

Practice 3

Laws of Exponents

Home Work.....

𝑎−2𝑏𝑎3𝑏−4

÷𝑎𝑏−1

𝑎−3𝑏−4

−18𝑐9𝑑20

12𝑐10𝑑6

16𝑎8𝑏4

2𝑎3𝑏 ÷𝑎2𝑏3𝑐36𝑎4𝑏𝑐5ษึ

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

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

0.00001452 0.00000000035468

..........................................................................................................................................................................................................................

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

..........................................................................................................................................................................................................................

0.000048 0.00000000021

.............................................................................................................

0.000038

.............................................................................................................

0.000000000000299

.............................................................................................................

69,100,000

.............................................................................................................

149,600,000

.............................................................................................................

Express each of the following numbers in scientific notation.

600,000,0005,300,000

.............................................................................................................

= ....................................................................................................................................................

149,600,000

0.000038

Example

Practice

Practice 5Sciencetific Notation

..........................................................................................................................................................................................................................

9.6 x 103 0.00456 x 10-7

..........................................................................................................................................................................................................................

0.000007 0.00478

..........................................................................................................................................................................................................................

15,234,000 94,251,000

..........................................................................................................................................................................................................................

12,100,000 110,000,000

..........................................................................................................................................................................................................................

0.5 x 109 7,000 x 103

..........................................................................................................................................................................................................................

0.00023 0.0000000094

Express each of the following as an integer or a decimal.

1.325 x 106 4.4 x 10-3

..........................................................................................................................................................................................................................

0.000048 0.00000000021

..........................................................................................................................................................................................................................

85,300 52,700,000

..........................................................................................................................................................................................................................

5,300,000 600,000,000

Homework

Sciencetific Notation

..........................................................................................................................................................................................................................

= ....................................................................................................................................................

..........................................................................................................................................................................................................................

(2.34 x 105) x (7.12 x 10-4) (13.4 x 104) ÷ (4 x 105)

..........................................................................................................................................................................................................................

(1.14 x 105) + (4.56 x 104) [(2.37 x 10-3) + (3.25 x 10-4)] ÷ (4.1 x 105)

..........................................................................................................................................................................................................................

(4.5 x 10-3) ÷ (9 x 10-1)

Practice

(4.2 x 10-4) x (2.6 x 102) (3.5 x 10-5) ÷ (1.4 x 108)

= ....................................................................................................................................................

Practice 6Apply Sciencetific Notation

Example

(7.2 x 103) x (2 x 1015) = ....................................................................................................................................................

..........................................................................................................................................................................................................................

(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)

..........................................................................................................................................................................................................................

(2.34 x 105) x (7.12 x 10-4) (13.4 x 104) ÷ (4 x 105)

..........................................................................................................................................................................................................................

(6.4 x 106) x (5.1 x 10-3) (2.17 x 10-5) ÷ (7 x 104)

..........................................................................................................................................................................................................................

(3.17 x 104) + (2.26 x 105) [(8.43 x 107) + (6.8 x 108)] ÷ (1.01 x 104)3

..........................................................................................................................................................................................................................

(2 x 105) - (0.12 x 107)(32.6 x 102) x (42.56 x 103)

(2.54 x 103) + (3.11 x 104) (6 x 105) - (3.1 x 103)

..........................................................................................................................................................................................................................

Homework

Sciencetific Notation

Law of Indices

Score: 50 marks

1.5) (253m7) x (1252m-3)

2.2) 125,040

2.3) 365,200,000,000

2.4) 0.000000465001

2.5) 0.000000000057306

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)

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

−27𝑐−8𝑑−21

34𝑐−30𝑑−4

𝑥−4(𝑎 + 𝑏)−8

𝑥−2(𝑎 + 𝑏)15

Law of Indices

..............................................................................................................................................................................................................

---------------------------------------------------------- Answer Sheet ----------------------------------------------------------------------

..............................................................................................................................................................................................................

Law of Indices

..............................................................................................................................................................................................................

---------------------------------------------------------- Answer Sheet ----------------------------------------------------------------------

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