Exponents Bundle 1 - Patchogue-Medford School District · 2019-09-12 · Exponent Review- Remember two things 1. You never multiply a base by its exponent. The exponent tells you

CCSS.Math.Content.8.EE.A.1

Know and apply the properties of integer exponents

to generate equivalent numerical expressions.

(These activities include Positive Exponents only.)

By Barbara Robinson-Rockin’ Middle School Math

https://www.teacherspayteachers.com/Store/Rockin-Middle-School-Math

Exponents Bundle 1

Property Investigations, Notes, Practice, Games,

Homework, and Test

http://www.corestandards.org/Math/Content/8/EE/A/1/


This Bundle includes the following activities:

1. Review of Exponents Practice Sheet

2. 3 Property Investigations (Discoveries):

Product of Powers Product of Quotients Power of Power

3. Interactive Notes: Includes a review of exponents and covers the 3 rules. Practice is provided on the notes

4. A Practice worksheet which covers Rule #1 and #2 only. You will probably

not cover all the rules on the first day. (This is two half sheets on one page) 5. A homework assignment which covers Rule #1 and #2 only. (This is two

half sheets on one page) 6. A Practice worksheet that covers all 3 rules 7. A Homework assignment that cover all 3 rules 8. A Partner Check practice 9. Game: I have, Who Has 10. Game: Connect 4 11. A Quiz or Test If you liked this Exponent Bundle, please see my Negative and Zero Exponent Bundle #2. You can find it at: https://www.teacherspayteachers.com/Product/Negative-and-Zero-Exponents-Bundle-2039460

https://www.teacherspayteachers.com/Product/Negative-and-Zero-Exponents-Bundle-2039460

https://www.teacherspayteachers.com/Product/Negative-and-Zero-Exponents-Bundle-2039460

Name ___________________________________ Date _________________________

Exponents Review

Write each number using exponents.

1) 6 x 6 = _________ 2) -5 x -5 x -5 x -5 = ____________

3) 27 = _________ 4) - (4 x 4 x 4) = ____________

5) a x a x a = _________ 6) 1

2 x

1

2 x

1

2 x

1

2 x

1

2 x

1

2 = ____________

7) -122 base _____ Expanded _______________ 8) (1

2)3 base ______ Expanded ________________

Exponent ______ Standard form ________ Exponent _______ Standard form __________

9) (-9)3 base _______ Expanded _______________________

Exponent _______ Standard form ___________

Write in expanded form.

10) 84 ______________________ 11) -32 ________________________________

12) 8 squared ____________________ 13) (-7)5 ________________________________

14) 7 cubed ______________________ 15) (3

4)5 ________________________________

Write in standard form.

16) 81 = ___________ 17) -24 = ______________

18) 4 squared = ___________ 19) (-2)4 = ______________

20) 5 cubed = ___________ 21) (-3)3 = ______________

22) (3

5)2 = ___________ 23) -33 = ______________

Write each expression in standard form. Then compare using <, >, or =.

24) 32 ______ 23 25) 73 ______ 7 x 7 x 7

26) 53 ______ 5 x 3 27) (-3)2 ______ -24

28) 2 squared ______ 2 cubed 29) 43 ______ 4 cubed

Circle the correct answer:

30) 48 in exponential notation: 86 68 480 481

31) Base is 4, Exponent is 5: 45 4 x 5 45 54


33) 23 + 34 57 2334 89 18

Key: Exponents Review


1) 6 x 6 = 62 2) -5 x -5 x -5 x -5 = (-5)4

3) 27 = 271 or 33 4) - (4 x 4 x 4) = -43

5) a x a x a = a3 6) 1

2 x

1

2 x

1

2 x

1

2 x

1

2 x

1

2 = (

𝟏

𝟐)6

7) -122 base 12 Expanded – (12 x 12) 8) (1

2)3 base (

𝟏

𝟐) Expanded (

𝟏

𝟐) 𝐱 (

𝟏

𝟐) 𝐱 (

𝟏

𝟐)

Exponent 2 Standard form -144 Exponent 𝟑 Standard form 𝟏

𝟖

9) (-9)3 base −𝟗 Expanded (−𝟗) 𝐱 (−𝟗) 𝐱 (−𝟗)

Exponent 3 Standard form -729

Write in expanded form.

10) 84 = 8 x 8 x 8 x 8 11) -32 = -(3 x 3)

12) 8 squared = 8 x 8 13) (-7)5 = (-7 x -7 x -7 x -7 x -7)

14) 7 cubed = 7 x 7 x 7 15) (3

4)5 = (

𝟑

𝟒) 𝐱 (

𝟑

𝟒) 𝐱 (

𝟑

𝟒) 𝐱 (

𝟑

𝟒) 𝐱 (

𝟑

𝟒)

Write in standard form.

16) 81 = 8 17) -24 = -16

18) 4 squared = 16 19) (-2)4 = 16

20) 5 cubed = 125 21) (-3)3 = -27

22) (3

5)2 =

𝟗

𝟐𝟓 23) -33 = -27

Write each expression in standard form. Then compare using <, >, or =.

24) 32 > 23 25) 73 = 7 x 7 x 7

26) 53 > 5 x 3 27) (-3)2 > -24

28) 2 squared < 2 cubed 29) 43 = 4 cubed

Circle the correct answer:


31) Base is 4, Exponent is 5: 45 4 x 5 45 54


33) 23 + 34 57 2334 89 18

KEY

Investigating Exponent Properties: Product of Powers

Expression Expand the expression Simplified

Expression 𝒂𝒃

52 ∙ 54 𝟓 ∙ 𝟓 ∙ 5 ∙ 5 ∙ 5 ∙ 5 56

84 ∙ 85

(−4)3 ∙ (−4)5

74 ∙ 74 ∙ 7

𝑥3 ∙ 𝑥7

5𝑥4𝑦2 ∙ 3𝑥6𝑦9

Try this one without expanding it.

Do you see a pattern that relates the expression in the first column to the

equivalent simplified expression? Write in words what you notice about the

exponents.

Try these on your own

715

9𝑥2𝑦 ∙ 8𝑥0𝑦5

Here is the formal rule when multiplying exponential expressions with

the same base:

Investigating Exponent Properties: Quotient of Powers

Expression Expanded form Cancel factors Simplified

Expression 𝒂𝒃

43

42

4 ∙ 4 ∙ 4

4 ∙ 4

4∙4∙𝟒

4∙4 41

36

33

15

14

𝑥9

𝑥7

615𝑦45

67𝑦25 Try this one without expanding it.



exponents.


Here is the formal rule when dividing exponential expressions with the

same base:

97

86𝑦5

83𝑦3

Investigating Exponent Properties: Power of a Power

Expression Expanded Form Expand further Simplified

Expression 𝒂𝒃

(92)3 92 ∙ 92 ∙ 92 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 96

(83)4

[(−6)2]5

(𝑥3)3

(𝑥4 ∙ 𝑦2)3

(𝑎20)32 Try this one without expanding it.



exponents.


424

(𝑥2𝑦5𝑧3)3

Here is the formal rule when multiplying exponential expressions by a

power:

Key: Investigating Exponent Properties: Product of Powers Expression Expand the expression Simplified

Expression 𝒂𝒃

52 ∙ 54 𝟓 ∙ 𝟓 ∙ 5 ∙ 5 ∙ 5 ∙ 5 56

84 ∙ 85 𝟖 ∙ 𝟖 ∙ 𝟖 ∙ 𝟖 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 89

(−4)3 ∙ (−4)5 (−𝟒) ∙ (−𝟒) ∙ (−𝟒) ∙ (−4) ∙ (−4) ∙ (−4)∙ (−4) ∙ (−4)

(−4)8

74 ∙ 74 ∙ 7 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 ∙ 𝟕 79

𝑥3 ∙ 𝑥2 𝒙 ∙ 𝒙 ∙ 𝒙 ∙ 𝑥 ∙ 𝑥 𝑥5

5𝑥4𝑦2 ∙ 3𝑥6𝑦9

Try this one without expanding it. 15𝑥10𝑦11



exponents.

When you multiply numbers that have the same base, add the exponents.


Answers will vary

715

9𝑥2𝑦 ∙ 8𝑥0𝑦5 9 ∙ 8 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 72𝑥2𝑦6


the same base: 𝒂𝒎 ∙ 𝒂𝒏 = 𝒂𝒎+𝒏

Key: Investigating Exponent Properties: Quotient of Powers

Expressio

n Expanded form Cancel factors

Simplified

Expression 𝒂𝒃

43

42

4 ∙ 4 ∙ 4

4 ∙ 4

4 ∙ 4 ∙ 𝟒

4 ∙ 4 41

36

33

3∙3∙3∙𝟑∙𝟑∙𝟑

3∙3∙3 33

15

14

1∙1∙1∙1∙𝟏

1∙1∙1∙1 11

𝑥9

𝑥7

𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝒙∙𝒙

𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥

𝑥2

615𝑦45

67𝑦25

Try this one without expanding it.

68𝑦20



exponents.

When you divide numbers that have the same base, subtract the

exponents. Try these on your own

Answers will vary

76

86𝑦5

83𝑦3 8∙8∙8∙8∙8∙8∙𝑦∙𝑦∙𝑦∙𝑦∙𝑦

8∙8∙8∙𝑦∙𝑦∙𝑦 83𝑦2


the same base: 𝒂𝒎

𝒂𝒏 = 𝒂𝒎−𝒏

Key: Investigating Exponent Properties: Power of a Power

Expression Expanded Form Expand further Simplified

Expression 𝒂𝒃

(92)3 92 ∙ 92 ∙ 92 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 ∙ 9 96

(83)4 83 ∙ 83 ∙ 83 ∙ 83 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8 ∙ 8

∙ 8

812

[(−6)2]5 (−6)2 ∙ (−6)2 ∙ (−6)2

∙ (−6)2 ∙ (−6)2

(−6) ∙ (−6) ∙ (−6) ∙ (−6)

∙ (−6) ∙ (−6) ∙ (−6) ∙ (−6)

∙ (−6) ∙ (−6)

(−6)10

(𝑥3)3 𝑥3 ∙ 𝑥3 ∙ 𝑥3 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 ∙ 𝑋 𝑥9

(𝑥4 ∙ 𝑦2)3 (𝑥4 ∙ 𝑦2) ∙ (𝑥4 ∙ 𝑦2) ∙

(𝑥4 ∙ 𝑦2)

𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥

∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 ∙ 𝑦 𝑥12𝑦6

(𝑎20)32 Try this one without expanding it. 𝑎640

Do you see a pattern that relates the expression in the first column to the equivalent

simplified expression? Write in words what you notice about the exponents.

When you multiply a power of a number times a power, multiply the exponents.


Answers will vary 424

(𝑥2𝑦5𝑧3)3 𝑥6𝑦15𝑧9

Here is the formal rule when multiplying exponential expressions by a

power: (𝒂𝒎)𝒏 = 𝒂𝒎 ∙ 𝒏

Notes: Exponential Rules

Exponent Review- Remember two things:

1. You never multiply a base by its exponent. The exponent tells you how many times to multiply

the base by itself. ∗ 43 is NOT 4 x 3. It is 4 x 4 x 4 = 64

2. If a base is negative, it must be in parentheses to use it when you multiply. Otherwise, your

answer will always be negative.

* (-3)4 means_________________________________________________________________

* −34 means __________________________________________________________________

YOUR TURN: Evaluate the exponential expression.

1. 53 = _________ 2. (2

3)

3 = _________ 3. (−6)3 = _________

4. 93 = _________ 5. −22 = _________ 6. 1.13 = _________

RULES OF EXPONENTS

Rule 1: Product of Powers 𝑎𝑚 ∙ 𝑎𝑛 = _____________

When ___________________ exponents with the same base, ________________ the exponents.

Ex: 43 ∙ 42 = ______ Why?

YOUR TURN: Simplify using exponents in your answer.

1) 32 ∙ 35 = _______ 2) (−4)3 ∙ (−4)8 = ________

3) (4)(46) = _________ 4) (−5)7 × (−5)3 × (−5)2 = ____________

Rule 2: Quotient of Powers 𝑎𝑚

𝑎𝑛= ___________

When ___________________ exponents with the same base, ______________ the exponents.

Ex: 36

34= _________ Why?


1) 69

65 = ________ 2)

(−18)10

(−18)2 = _______

3) 108 ÷ 104 = _________ 4) 95 ÷ 9 = _________

Rule 3: Power of a Power (𝑎𝑚)𝑛 = ____________

When finding the power of a power, ________________ the exponents.

Ex: = (63)4 = _______ Why?


1) (84)3 = __________ 2) (152)8 = __________

3) [(−4)6]2 = _________ 4) (93)5 = __________

REVIEW:

1) (−15)6 ∙ (−15)3 ∙ (−15) = _______ 2) [(−8)7]6 = _________

3) (−5)⁸

(−5)³ = _____ 4) (78)2 = ________

5) (41)5 = ________ 6) 34 ∙ 36 = __________

7) 65 × 62 = _________ 8) 1012

104 = __________

9) (−12)10 ÷ (−12)2 = __________ 10) 85 × 8 = ___________

Challenge:

11) 102 x 106

107 = __________ 12) 54 ∙ 56

54 = __________

13) 75x 73

7 x 72 = __________ 14) 47∙ 43

48÷ 42 = ___________

15) (36)2

(33)4 = __________ 16) 28∙ 23 x 2

26 ∙ 23 ∙ 22 = ___________

Key: Notes Exponential Rules

Exponent Review- Remember two things

1. You never multiply a base by its exponent. The exponent tells you how many times to multiply

the base by itself. ∗ 43 is NOT 4 x 3. It is 4 x 4 x 4 = 64

2. If a base is negative, it must be in parentheses to use it when you multiply. Otherwise, your

answer will always be negative.

* (-3)4 means -3 x -3 x -3 x -3 = 81

* −34 means negative or the opposite of (3 x 3 x 3 x 3) = -81

YOUR TURN: Evaluate the exponential expression.

1. 53 = 125 2. (2

3)

3 =

8

27 3. (−6)3 = -216

4. 93 = 729 5. −22 = -4 6. 1.13 = 1.331

RULES OF EXPONENTS

Rule 1: Product of Powers 𝑎𝑚 ∙ 𝑎𝑛 = 𝑎𝑚+𝑛

When multiplying exponents with the same base, add the exponents.

Ex: 43 ∙ 42 = 45 Why? (4 x 4 x 4) x (4 x 4) = 45 or 43+2 = 45


1) 32 ∙ 35 = 37 2) (−4)3 ∙ (−4)8 = (−4)11

3) (4)(46) = 47 4) (−5)7 × (−5)3 × (−5)2 = (−5)12

Rule 2: Quotient of Powers 𝑎𝑚

𝑎𝑛= 𝑎𝑚−𝑛

When dividing exponents with the same base, subtract the exponents.

Ex: 36

34= 32 Why?

3 𝑥 3 𝑥 3 𝑥 3 𝑥 3 𝑥 3

3 𝑥 3 𝑥 3 𝑥 3 = 32 or 36−4 = 32


2) 69

65 = 64 2)

(−18)10

(−18)2 = (−18)8

3) 108 ÷ 104 = 104 4) 95 ÷ 9 = 94

KEY

Rule 3: Power of a Power (𝑎𝑚)𝑛 = 𝒂𝒎 𝐱 𝒏

When finding the power of a power, multiply the exponents.

Ex: (63)4 = 𝟔𝟏𝟐 Why? 𝟔𝟑 x 𝟔𝟑 x 𝟔𝟑 x 𝟔𝟑 = (6x6x6) x (6x6x6) x (6x6x6) x (6x6x6) = 𝟔𝟏𝟐

𝟔𝟑 𝐱 𝟒 = 𝟔𝟏𝟐


2) (84)3 = 812 2) (152)8 = 1516

4) [(−4)6]2 = (−4)12 4) (93)5 = 915

Your Turn Review:

1) (−15)6 ∙ (−15)3 ∙ (−15) = (−15)10 2) [(−8)7]6 = (−8)42

3) (−5)⁸

(−5)³ = (−5)5 4) (78)2 = 716

5) (41)5 = 45 6) 34 ∙ 36 = 310

7) 65 × 62 = 67 8) 1012

104 = 108

9) (−12)10 ÷ (−12)2 = (−12)8 10) 85 × 8 = 86

Challenge:

11) 102 x 106

107 = 101 12)

54 ∙ 56

54 = 56

13) 75x 73

7 x 72 = 75 14)

47∙ 43

48÷ 42 = 44

15) (36)2

(33)4 = 30 = 1 16) 28∙ 23 ∙ 2

26 ∙ 23 ∙ 22 = 21

KEY

Name _______________________________ Date ___________________

Practice: Exponents Review and Rules #1 and #2


1) 5 x 5 = _______ 2) -5 x -5 x -5 x -5 = _______

3) - (2 x 2 x 2) = _______ 4) n x n x n x n x n x n = _______

Evaluate:

5) -83 = _______ 6) (-3)2 = _______ 7) (-4)3 =________ 8) -162 = _______

9) (-7)3 = _______ 10) (-12)2 = _______ 11) (-10)5 = _______ 12) -14 = _______

Use the rules of exponents to simplify the expression with exponents:

13) 64 • 62 = _______ 14) 31 • 32 = _______ 15) 811 • 84 = _______ 16) 90 • 94 ______

17) 48 • 48 = _______ 18) 15 • 13 • 16 = _______ 19) 2

6

10

10 = _______ 20)

1

3

5

5 = _______

21) 4

5

8

8 =_______ 22)

2

4

2

2 = _______ 23)

2

7

7

7 = _______ 24)

4

10

4

4 = _______

Name _______________________________ Date ___________________

Practice: Exponents Review and Rules #1 and #2


1) 5 x 5 = _______ 2) -5 x -5 x -5 x -5 = _______

3) - (2 x 2 x 2) = _______ 4) n x n x n x n x n x n = _______

Evaluate:

5) -83 = _______ 6) (-3)2 = _______ 7) (-4)3 =________ 8) -162 = _______

9) (-7)3 = _______ 10) (-12)2 = _______ 11) (-10)5 = _______ 12) -14 = _______


13) 64 • 62 = _______ 14) 31 • 32 = _______ 15) 811 • 84 = _______ 16) 90 • 94 ______

17) 48 • 48 = _______ 18) 15 • 13 • 16 = _______ 19) 2

6

10

10 = _______ 20)

1

3

5

5 = _______

21) 4

5

8

8 =_______ 22)

2

4

2

2 = _______ 23)

2

7

7

7 = _______ 24)

4

10

4

4 = _______

Key to Practice: Exponents Review and Rules #1 and #2


1) 5 x 5 = 52 2) -5 x -5 x -5 x -5 = (-5)4

3) - (2 x 2 x 2) = -23 4) n x n x n x n x n x n = n6

Evaluate:

5) -83 = -512 6) (-3)2 = 9 7) (-4)3 = -64 8) -162 = -256

9) (-7)3 = -343 10) (-12)2 = 144 11) (-10)5 = -100,000 12) -14 = -1


13) 64 • 62 = 66 14) 31 • 32 = 33 15) 811 • 84 = 815 16) 90 • 94 = 94

17) 48 • 48 = 416 18) 15 • 13 • 16 = 114 19) 2

6

10

10 = 104 20)

1

3

5

5 = 52

21) 4

5

8

8 = 81 22)

2

4

2

2 = 22 23)

2

7

7

7 = 75 24)

4

10

4

4 = 46

KEY

Name: ________________________________ Date: ____________________

Homework: Exponents Review and Rules #1 and #2

Simplify:

1. (3

5)

2= _______ 2. -72 = _______ 3. 31 = _______ 4. (-7)2 = _______

Write the answer in Exponential form:

5. 68 ÷ 65 = _______ 6. 8

8

6

6 = _______ 7. (-8)4 • (-8)4 = _______ 8.

7

8

7

7= _______

9. 74 x 73 = _______ 10. (-7)4 ÷ (-7) 3 = _______ 11. 84 • 8 = ______ 12. 4

5

8

8 = _______

13. 4

8

3

3 = _______ 14. 62 x 69 x 6 = _______ 15. (-2)4 • (-2)4 = _______ 16.

(−8)5

(−8)2= _______

17. (-3)4 x (-3)4 x (-3)4 x (-3)4 = _____ 18. 5 cubed =_____ 19. 8

8

3

3=______ 20. 4 squared = _____

Name: ________________________________ Date: ____________________

Homework: Exponents Review and Rules #1 and #2

Simplify:

1. (3

5)

2= _______ 2. -72 = _______ 3. 31 = _______ 4. (-7)2 = _______


5. 68 ÷ 65 = _______ 6. 8

8

6

6 = _______ 7. (-8)4 • (-8)4 = _______ 8.

7

8

7

7= _______

9. 74 x 73 = _______ 10. (-7)4 ÷ (-7) 3 = _______ 11. 84 • 8 = ______ 12. 4

5

8

8 = _______

13. 4

8

3

3 = _______ 14. 62 x 69 x 6 = _______ 15. (-2)4 • (-2)4 = _______ 16.

(−8)5

(−8)2= _______

17. (-3)4 x (-3)4 x (-3)4 x (-3)4 = _____ 18. 5 cubed =_____ 19. 8

8

3

3=______ 20. 4 squared = _____

Key to Homework: Exponents Review and Rules #1 and #2

Simplify:

1. (3

5)

2= 𝟗

𝟐𝟓 2. -72 = -49 3. 31 = 𝟑 4. (-7)2 = 49


5. 68 ÷ 65 = 63 6. 8

8

6

6 = 60 7. (-8)4 • (-8)4 = (-8)8 8.

7

8

7

7= 71

9. 74 x 73 = 77 10. (-7)4 ÷ (-7) 3 = (-7)1 11. 84 • 8 = 85 12. 4

5

8

8 = 81

13. 4

8

3

3 = 34 14. 62 x 69 x 6 = 612 15. (-2)4 • (-2)4 = (-2)8 16.

(−8)5

(−8)2= (-8)3

17. (-3)4 x (-3)4 x (-3)4 x (-3)4 = (-3)16 18. 5 cubed =53 19. 8

8

3

3= 30 20. 4 squared = 42

KEY

Name _________________________________________ Date ___________________

Practice: Rules of Exponents

Review: Write the answer in standard form:

1) 53 = 2) 8 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 =

3) (−6)2 = 4) 9 𝑐𝑢𝑏𝑒𝑑 =

5) − 44 = 6) 21 =

7) − 43 = 8) (−3)3 =

Rule #1: Product of Powers Property 𝒂𝒎 ∙ 𝒂𝒏 = 𝒂𝒎+𝒏

9) 53 × 56 = 10) 72 ∙ 77 ∙ 73 =

11) 3 × 34 = 12) (−8)11 ∙ (−8)2 =

13) 9 × 92 = 14) 𝑥8 ∙ 𝑥8 =

Rule #2: Quotient of Powers Property 𝒂𝒎

𝒂𝒏= 𝒂𝒎−𝒏

15) 53

51= 16)

(−7)6

(−7)2=

17) 24

22= 18)

𝑛15

𝑛5=

19) 85 ÷ 84 = 20) (−9)5 ÷ (−9)5 =

Rule #3: Power of Power Property (𝒂𝒎)𝒏 = 𝒂𝒎∙𝒏

21) (53)6 = 22) (𝑛3)5 =

23) (22)6 = 24) [(−5)3]2 =

Mixed Practice/Review:

25) 32 ∙ 3 ∙ 35 = 26) 610

65=

27) 𝑛9 ÷ 𝑛2 = 28) 58 × 52 =

29) (23)3 = 30) [(−4)2]9 =

Make up two problems of your own examples for Rule #1. (answer them too).

31) 32)


33) 34)


35) 36)

Name _________________________________________ Date ___________________

Answer Key: Rules of Exponents

Review: Write the answer in standard form:

2) 53 = 125 2) 8 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 = 64

3) (−6)2 = 36 4) 9 𝑐𝑢𝑏𝑒𝑑 = 729

5) − 44 = -256 6) 21 = 2

7) − 43 = -64 8) (−3)3 = -27

Rule #1: Product of Powers Property 𝒂𝒎 ∙ 𝒂𝒏 = 𝒂𝒎+𝒏

9) 53 × 56 = 59 10) 72 ∙ 77 ∙ 73 = 712

11) 3 × 34 = 35 12) (−8)11 ∙ (−8)2 = (−8)13

13) 9 × 92 = 93 14) 𝑥8 ∙ 𝑥8 = 𝑥16

Rule #2: Quotient of Powers Property 𝒂𝒎

𝒂𝒏= 𝒂𝒎−𝒏

15) 53

51= 52 16)

(−7)6

(−7)2= (−7)4

17) 24

22= 22 18)

𝑛15

𝑛5= 𝑛10

19) 85 ÷ 84 = 81 20) (−9)5 ÷ (−9)5 = (−9)0 which = 1

Rule #3: Power of Power Property (𝒂𝒎)𝒏 = 𝒂𝒎∙𝒏

21) (53)6 = 518 22) (𝑛3)5 = 𝑛15

23) (22)6 = 212 24) [(−5)3]2 = (−5)6

Mixed Practice/Review:

25) 32 ∙ 3 ∙ 35 = 38 26) 610

65= 65

27) 𝑛9 ÷ 𝑛2 = 𝑛7 28) 58 × 52 = 510

29) (23)3 = 29 30) [(−4)2]9 = (−4)18

#31-36 Answers will vary

KEY

Name: _____________________________ Date:___________________

HW: Rules of Exponents

Fill in the blanks using expanded form to prove the answer is correct.

#1. 63 ∙ 62 = 65 #2. 76

74 = 72

(____ ∙ ____ ∙ ____) ∙ (____ ∙ ____) = 65

= 72

#𝟑. (32)4 = 38

32 ∙ ______ ∙ ______ ∙ ______ = _______

(____ ∙ ____) ∙ (____ ∙ ____) ∙ (____ ∙ ____) ∙ (____ ∙ ____) = 38

Fill in the blanks with the correct words. Then use the rule to simplify the example.

Rule #1 _______________________________________

When _______________exponents with the same base, 𝐄𝐱: 𝟗𝟕 ∙ 𝟗𝟐 = ______

____________ the exponents.

Rule #2 _______________________________________

When ________________ exponents with the same base, Ex: 𝟐𝟏𝟎

𝟐𝟒= _____

___________________ the exponents.

Rule #3 _______________________________________

When raising a ____________ to a ______________, Ex: [(−𝟓)𝟐]𝟏𝟑 ______

____________________ the exponents.

Practice

Simplify using exponential form for your answer.

1) 65 ∙ 65 =_______ 2) (−5)10

(−5)2= _________ 3)

83

81= _________

4) (73)4= _______ 5) (−4)4 ∙ (−4)3 =_______ 6) [(−2)4]4 = ________

Key- HW: Rules of Exponents

Fill in the blanks using expanded form to prove the answer is correct.

#1. 63 ∙ 62 = 65 #2. 76

74 = 72

(6 ∙ 6 ∙ 6) ∙ (6 ∙ 6) = 65 7∙7 ∙7 ∙7∙7∙7

∙7 ∙7 ∙7∙7 = 72

#𝟑. (32)4 = 38

32 ∙ 32 ∙ 32 ∙ 32 = 38

(3 ∙ 3) ∙ (3 ∙ 3) ∙ (3 ∙ 3) ∙ (3 ∙ 3) = 38

Fill in the blanks with the correct words. Then use the rule to simplify the example.

Rule #1 Product of Powers

When multiplying exponents with the same base, 𝐄𝐱: 𝟗𝟕 ∙ 𝟗𝟐 = 𝟗𝟗

add the exponents.

Rule #2 Quotient of Powers

When dividing exponents with the same base, Ex: 𝟐𝟏𝟎

𝟐𝟒 = 𝟐𝟔

subtract the exponents.

Rule #3 Power of a Power

When raising a power to a power, Ex: [(−𝟓)𝟐]𝟏𝟑 = (−𝟓)𝟐𝟔

multiply the exponents.

Practice

Simplify using exponential form for your answer.

1) 𝟔𝟓 ∙ 𝟔𝟓 = 𝟔𝟏𝟎 2) (−𝟓)𝟏𝟎

(−𝟓)𝟐= (−𝟓)𝟖 3)

𝟖𝟑

𝟖𝟏= 𝟖𝟐

4) (𝟕𝟑)𝟒= 𝟕𝟏𝟐 5) (−𝟒)𝟒 ∙ (−𝟒)𝟑 = (−𝟒)𝟕 6) [(−𝟐)𝟒]𝟒 = (−𝟐)𝟏𝟔

KEY

Simplify Exponential Expressions Partner Check

Directions: Cut the paper on the vertical line. Each partner gets one side. Complete your problem by simplifying the expression using exponents. Then stop, trade papers, and check your partner’s answer. Help each other correct any mistakes and then continue the process again until all problems are complete.

Name: ______________________________ Name: _______________________________

1. 34 ∙ 3 ∙ 33 2. (−5)6 ∙ (−5)4

STOP

3. [(−7)5]8 4. (26)4

STOP

5. 69

64 ∙ 63 6.

33 ∙ 34

3

STOP

7. (23)6 × (22)2

8. (83)4 × (82)5

STOP

9. 411

47× 410

10. 65

64× 62

STOP

11. (25)

4

(24)3 12. (74)

2

73

STOP

13. The Robinson toy company sold 108 boxes of Silly Bands. Each box of Silly Bands contains 104 Silly Bands. How many Silly Bands did they sell?

14. A warehouse contains 65 containers. Each container weighs 63 pounds. How much is the weight inside all of the containers?

STOP

15. A farm has 84 pigs. If all of the pigs weigh a total of 86 pounds, what is the average weight of each pig?

16. Jim wrote 107 words during a period of 103 days. On average, how many words did Jim write per day? STOP

KEY: Simplify Exponential Expressions Partner Check

Directions: Cut the paper on the vertical line. Each partner gets one side. Complete your problem by simplifying the expression using exponents. Then stop, trade papers, check your partner’s answer. Help each other correct any mistakes and then continue the process again until all problems are complete.

1. 34 ∙ 3 ∙ 33 𝟑𝟖

2. (−5)6 ∙ (−5)4 (−𝟓)𝟏𝟎

STOP

3. [(−7)5]8 (−𝟕)𝟒𝟎 4. (26)4 𝟐𝟐𝟒

STOP

5. 69

64 ∙ 63 𝟔𝟐 6.

33 ∙ 34

3 𝟑𝟔

STOP

7. (23)6 × (22)2 𝟐𝟐𝟐

8. (83)4 × (82)5 𝟖𝟐𝟐

STOP

9. 411

47× 410 𝟒𝟏𝟒

10. 65

64× 62 𝟔𝟑

STOP

11. (25)

4

(24)3 𝟐𝟖 12. (74)

2

73 𝟕𝟓

STOP

13. The Robinson toy company sold 108 boxes of Silly Bands. Each box of Silly Bands contains 104 Silly Bands. How many Silly Bands did they sell?

𝟏𝟎𝟏𝟐 Silly Bands

14. A warehouse contains 65 containers. Each container weighs 63 pounds. How much is the weight inside all of the containers?

𝟔𝟖 pounds STOP

15. A farm has 84 pigs. If all of the pigs weigh a total of 86 pounds, what is the average weight of each pig?

𝟖𝟐 pounds

16. Jim wrote 107 words during a period of 103 days. On average, how many words did Jim write per day?

𝟏𝟎𝟒 words per day STOP

KEY

I Have, Who Has?

Use this I have, Who Has game to review Exponents and Exponential Rules.

Product of Powers

Product of Quotients

Power of Power

Rules:

The game can be played with either whole class or with a small group.

First you must cut out the cards. Then pass out the cards to all members of the

group. It does not matter if they place them facing up or down. Start with any

card placed in the center. (If playing with the whole class, place the card on the

overhead projector.)

Start with any card. Read out the “Who Has____?” on the first card. Each player

looks to see if they have the corresponding answer. Whoever has it places it beside

the first card and reads out “I have____” and then “Who has____?” on that card.

Play continues until the last card is read. It will match the first card that was

played.

Game Variation-Pairs Dominos:

Each pair of students gets a set of cards. One player shuffles and deals out the

cards. The dealer picks one of her cards face up on the corner of her desk. Both

players then search through their hand to see if he/she has the card that is the

answer to the first card. Whomever has the next card, then places it either next

to or under the first card. Now both players look through their hand to search for

the answer to the problem on the 2nd card. This continues until all cards are played.

The winner could be whomever runs out of cards first (pure luck), or both players

win if they have a correct train of dominos on their desk.

Game Variation-Scavenger Hunt:

Place the cards around the room. Students can start anywhere and then find the

answer on the next card until they reach back to the beginning.

I have 𝟓𝟓

Who has? 𝟑𝟑

𝟑𝟏

I have −𝟐𝟕

Who has? – (𝟑)𝟒

I have 𝟑𝟐

Who has?

(𝟓𝟑)𝟑

I have -81

Who has?

6 squared

I have 𝟓𝟗

Who has? 𝟕𝟐 𝐱 𝟕

I have 𝟔𝟐

Who has? (−𝟑)𝟐 ∙ (−𝟑)𝟒 ∙ (−𝟑)

I have 𝟕𝟑

Who has? (−𝟖)𝟐 ∙ (−𝟖)𝟔

I have (−𝟑)𝟕

Who has? 𝟔𝟓 ÷ 𝟔𝟓

I have (−𝟖)𝟖

Who has? 𝟖𝟓 ÷ 𝟖𝟐

I have 𝟔𝟎

Who has? (𝟔𝟒)𝟒

I have 𝟖𝟑

Who has? 𝟐𝟖

𝟐𝟒

I have 𝟔𝟏𝟔

Who has? (−𝟗)𝟔

(−𝟗)𝟒

I have 𝟐𝟒

Who has? [(−𝟑)𝟓]𝟒

I have (−𝟗)𝟐

Who has? (−𝟑)𝟓 𝐱 (−𝟑)𝟒

I have (– 𝟑)𝟐𝟎

Who has? 𝟒𝟐 ∙ 𝟒𝟑

I have (−𝟑)𝟗

Who has? 𝟏𝟏𝟒

𝟏𝟕

I have 𝟒𝟓

Who has?

9 cubed

I have 𝟏𝟕

Who has? 𝟐𝟒 𝐱 𝟐𝟓

𝟐𝟑

I have 𝟗𝟑

Who has? 𝟑 ∙ 𝟑 ∙ 𝟑 ∙ 𝟑 ∙ 𝟑

I have 𝟐𝟔

Who has? 𝟐𝟏

I have 𝟑𝟓

Who has? 𝟓𝟕

𝟓

I have 𝟐

Who has? 𝟒𝟏𝟐

𝟒𝟒

I have 𝟓𝟔

Who has? 𝟒𝟐 ∙ 𝟒

I have 𝟒𝟖

Who has? (−𝟑)𝟒

I have 𝟒𝟑

Who has? 𝟏𝟗 𝐱 𝟏𝟑

I have 𝟖𝟏

Who has? 𝟕𝟔 𝐱 𝟕𝟔𝐱 𝟕𝟔

I have 𝟏𝟏𝟐

Who has? 𝟐𝟏𝟐

𝟐𝟓

I have 𝟕𝟏𝟖

Who has? 𝟓𝟑

I have 𝟐𝟕

Who has? (– 𝟑)𝟑

I have 𝟏𝟐𝟓

Who has? 𝟓𝟐 ∙ 𝟓𝟑

Connect 4: Exponential Rules Game Board

You and a partner will take turns choosing and giving an answer using exponential form. Ex. ( 𝑎𝑏) If

you are correct, you will place a chip on the block. If incorrect, your partner can steal the block if

he/she simplifies it correctly. If you disagree about the answer, ask your teacher. First player to get

four in a row, wins.

Materials needed: Game board, chips of 2 different colors.

95 ÷ 9

[(−9)2]²

(−6)9

(−6)3

710

• 76

76

• 76

45 • 47

210 x 25

28

÷ 26

(43)4•(42)2

𝑎8 • 𝑎2

(32)6

34

77

75

95 x 92

90

𝑥14

𝑥2

𝑥10 • 𝑥2

𝑥4 • 𝑥3• 𝑥6

23

• 27

24

• 25

(𝑎2)6

(𝑥2)3 • 𝑥6

126 • 123

𝑏5 ÷ 𝑏3

46

43

56x 57

54

75 • 79

16

• 17

13

69

60

(43)4• 47

75 ÷ 75

218 ÷ 25

24

• 26

[(−1)6]²

33

32

28• 22• 22

310

• 32

34

• 36

(−8)10

(−8)2

513• 52• 5

59 x 51

(52)4

82 • (82)4

610

68

x8y7 x6y7

Key-Connect 4: Exponential Rules

You and a partner will take turns choosing and giving an answer using exponential form. Ex. ( 𝑎𝑏) If you are

correct, you will place a chip on the block. If incorrect, your partner can steal the block if he/she simplifies it

correctly. If you disagree about the answer, ask your teacher. First player to get four in a row, wins.

Materials needed: Game board, chips of 2 different colors.

95 ÷ 9

94

[(−9)2]²

(−9)4

(−6)9

(−6)3

(−6)6

710

• 76

76

• 76

74

45 • 47

412

210 x 25

28

÷ 26

213

(43)4•(42)2

416

𝑎8 • 𝑎2

𝑎10

(32)6

34

38

77

75

72

95 x 92

90

97

𝑥14

𝑥2

𝑥12

𝑥10 • 𝑥2

𝑥4 • 𝑥3• 𝑥6

𝑥11

23

• 27

24

• 25

21

(𝑎2)6

𝑎12

(𝑥2)3 • 𝑥6

𝑥12

126 • 123

129

𝑏5 ÷ 𝑏3

𝑏2

46

43

43

56x 57

54

59

75 • 79

714

16

• 17

13

110

69

60

69

(43)4• 47

419

75 ÷ 75

70

218 ÷ 25

24

• 26

23

[(−1)6]²

(−1)12

33

32

31

28• 22• 22

212

310

• 32

34

• 36

32

(−8)10

(−8)2

(−8)8

513• 52• 5

516

59 x 51

(52)4

52

82 • (82)4

810

610

68

62

x8y7 x6y7

x14y14

KEY

Name:_________________________________________ Date:___________________________

Exponent Test

Fill in the blanks 1) When multiplying exponents with the same base, you ___________ the exponents.

2) When __________________ exponents with the same base, you subtract the exponents.

3) When finding the power of a power, you _____________________ the exponents.

Simplify #4-9 completely. 4) (−3)4 = ________ 5) −34 = ________ 6) (−20) 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 = ________

7) (−2)3 = ________ 8) (−5) 𝑐𝑢𝑏𝑒𝑑 = ________ 9) −23 = ___________

In #10-24, use your exponent rules to provide an answer in EXPONENT form.

22) Simplify: 24∙26

25 = ___________________

23) Simplify: 𝑥4∙𝑥6

𝑥3∙𝑥3 = _____________________

24) Simplify: 24 ∙ 26 ∙ (23)3 = ____________

10) 25 24 Answer: ___________

11) [(–3)5]3 Answer: ___________

12) (-12)4 (-12)6 Answer: ___________

13) 25017 250 Answer: ___________

14) 810 82 Answer: ___________

15) (z3)6 Answer: ___________

16) y20 y5 Answer: ___________

17) 137 13 133 Answer: ___________

18) (92)7

Answer: ___________

19) (–7)3 (–7)3 Answer: ___________

20) x15 x6 Answer: ___________

21) (656)6 Answer: ___________

Applications of Exponents Write the mathematical expression (Ex: 𝟐𝟑 ∙ 𝟐𝟓) and the answer with exponents and also in standard form including units. 25) A chicken plant receives 56 chickens daily. Each of the company trucks drop off 54

chickens once a day. How many trucks drop off chickens during the day? 26) Each large bag of potato chips has 122 chips in the bag. The grocery store

has 123 bags of potato chips in the store. How many potato chips are in the store all together?

27) The walk-in closets at a condo are cubes (meaning the length,

width, and height of the room are equivalent). The length of the closet is 8 feet. What is the volume of the closet? (Reminder: volume = length width height or s3)

28) A park has a fenced in area for people to let their dogs run

around without a leash. The enclosure is a square with side length 40ft. What is the area of the fenced in region?

*BONUS QUESTION*

Simplify this expression: Simplify: –4x5y4z 5xy7z4= ___________________

Key: Exponent Test Fill in the blanks 1) When multiplying exponents with the same base, you add the exponents.

2) When dividing exponents with the same base, you subtract the exponents.

3) When finding the power of a power, you multiply the exponents.

Simplify #4-9 completely. 4) (−3)4 = 81 5) −34 = −81 6) (−20) 𝑠𝑞𝑢𝑎𝑟𝑒𝑑 = 400

7) (−2)3 = −8 8) (−5)𝑐𝑢𝑏𝑒𝑑 = −125 9) −23 = -8

In #10-24, use your exponent rules to provide an answer in EXPONENT form.

22) Simplify: 24∙26

25 = 25

23) Simplify: 𝑥4∙𝑥6

𝑥3∙𝑥3 = 𝑥4

24) Simplify: 24 ∙ 26 ∙ (23)3 = 219

10) 25 24 Answer: 29

11) [(–3)5]3 Answer: (-3)15

12) (-12)4 (-12)6 Answer: (-12)10

13) 25017 250 Answer: 25016

14) 810 82 Answer: 88

15) (z3)6 Answer: z18

16) y20 y5 Answer: y15

17) 137 13 133 Answer: 1311

18) (92)7

Answer: 914

19) (–7)3 (–7)3 Answer: (-7)0

20) x15 x6 Answer: x21

21) (656)6 Answer: 6536

KEY

Applications of Exponents Write the mathematical expression (Ex: 𝟐𝟑 ∙ 𝟐𝟓) and the answer with exponents and also in standard form including units. 25) A chicken plant receives 56 chickens daily. Each of the company trucks drop off 54 chickens once a day. How many trucks drop off chickens each day? 56

54 = 52 = 25 trucks

26) Each large bag of potato chips has 122 chips in the bag. The grocery store has 123 bags of potato chips in the store. How many potato chips are in the store all together? 122 123 = 125 = 248,832 potato chips 27) The walk-in closets at a condo are cubes (meaning the length, width, and height of the room are equivalent). The length of the closet is 8 feet. What is the volume of the closet? (Reminder: volume = length width height or s3) 8 x 8 x 8 = 83 = 512 ft3 28) A park has a fenced in area for people to let their dogs run around without a leash. The enclosure is a square with side length 40ft. What is the area of the fenced in region? 40 x 40 = 402 = 1,600 ft2

*BONUS QUESTION*

Simplify this expression: Simplify: –4x5y4z 5xy7z4= –20x6y11z5

KEY

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Documents

Exponents Bundle 1 - Patchogue-Medford School District · 2019-09-12 · Exponent Review- Remember two things 1. You never multiply a base by its exponent. The exponent tells you