1

Ms. Campos - Math 8

Unit 3 – Exponents

2017-2018

Name __________________________ #_____

Date Lesson Topic Homework

M 5 10/16 1 Introduction to Exponents Lesson 1 – Page 4

T 6 10/17 2 Zero and Negative Exponents Lesson 2 – Page 8

W 1 10/18 3 Multiplying Exponents Lesson 3 – Page 11

T 2 10/19 4 Multiplying with Coefficients Lesson 4 –Page 14

F 3 10/20 5

Distribution Property with Exponents Quiz – Lesson 1-4

Lesson 5 –Page 17

M 4 10/23 6 Power to a Power Lesson 6 – Page 20

T 5 10/24 7 Dividing Exponents Lesson 7 –Page 23

W 6 10/25 8 Dividing Polynomials Family Connect Night

T 1 10/26 9 Mixed Review Finish Mixed Review

F 2 10/27 10

Quiz – Mixed Review Activity

Review Sheet- Odd Numbers

M 3 10/30

Review Finish Review Sheet and Check Answers on Website

T 4 10/31 Test

2

Unit 3 – Lesson 1

Aim: I can identify and simplify exponential expressions.

Warm Up: Answer Questions in boxes.

4x² + 7 2 6

1) Name the variable _______ 4) Name the base ______ 1) What is the base _________

2) Name the coefficient _______ 5) Name the constant ______ 2) What is the exponent ________

3) Name the exponent ________

Guided Practice:

Base – When a number is raised to a power, the number that is used as a factor is the base.

Exponential Form – A number written with a base and an exponent.

Expanded form – A number written as the sum of the values of its digits.

Compute – Solve. Get an answer.

Examples: Write the following in exponential form:

1) 5 × 5 × 5 × 5 × 5 × 5 ____________ 2) 7

9

7

9

7

9 ____________

3) 2𝑥 ∙ 2𝑥 ∙ 2𝑥 ∙ 9 ∙ 9 ____________ 4) 4 ∙ 4 ∙ 𝑥 ∙ 𝑥 ∙ 𝑥 ____________

Exponent Notation: Check for Understanding

5) 4 × ⋯× 4⏟ 7 𝑡𝑖𝑚𝑒𝑠

= ______ 6) 3.6 × ⋯× 3.6⏟ _______ 𝑡𝑖𝑚𝑒𝑠

= 3.647

7) (−11.63) ×⋯× (−11.63)⏟ 34 𝑡𝑖𝑚𝑒𝑠

= _________ 8) 12 ×⋯× 12⏟ _______𝑡𝑖𝑚𝑒𝑠

= 1215

9) (−5) × ⋯× (−5)⏟ 10 𝑡𝑖𝑚𝑒𝑠

= ________ 10) 7

2×⋯×

7

2⏟ 21 𝑡𝑖𝑚𝑒𝑠

= ______

11) (−13) ×⋯× (−13)⏟ 6 𝑡𝑖𝑚𝑒𝑠

= ________ 12) (−1

14) × ⋯× (−

1

14)⏟

10 𝑡𝑖𝑚𝑒𝑠

= __________

3

13) 𝑥 ∙ 𝑥⋯𝑥⏟ 185 𝑡𝑖𝑚𝑒𝑠

= _______ 14) 𝑥 ∙ 𝑥⋯𝑥⏟ _______𝑡𝑖𝑚𝑒𝑠

= 𝑥𝑛

Is it necessary to do all of the calculations to determine the sign of the product? Why or why not?

15) (−5) × (−5) × ⋯× (−5)⏟ 95 𝑡𝑖𝑚𝑒𝑠

= (−5)95 16) (−1.8) × (−1.8) × ⋯× (−1.8)⏟ 122 𝑡𝑖𝑚𝑒𝑠

= (−1.8)122

Problem set:

Write in expanded form and compute the value:

17) 36 18) (−2)4 19) (−

4

11)5

20) 92 21) -42 22) −(

1

2)3

Write the following in exponential form:

13) 1

4×1

4 14)

7

9

7

9

7

9 15)

1

3×1

3×1

𝑥×1

𝑥×1

𝑥

Write in expanded form.

16) (2x)3 17) (3x)2 18) (7x)4

19) What do exponents represent?

Exit Ticket:

4

Unit 3 – Lesson 1 Homework

1) Solve the equation 2(4x + 8) = 7x – 20 2) Solve: 3

5𝑥 + 4 =

1

3(3𝑥 + 9)

3) Which of the following equations has no solution?

A) 3x + 15 = 3(x + 5) B) 3x + 7 = 2x + 7 C) 3x + 5 = 3(x+5) D) 3x + 9 = 15

4) Marty has $80 to spend at a sporting goods store. He will spend $56 on a shirts, and then buy some darts.

Each box of darts costs $6. He want to buy as many boxes as possible. Which equation shows how to find the

number of boxes of darts, x, he can buy?

A) 80 = 56 + 6x B) 80 = 56 – 6x C) 80 = (56)(6x) D) 80 = 56

6𝑥

5) Write an algebraic expression to represent 4 less than twice a number, n?

6) What is the value of 12 + 2(12 – 9)2 7) Solve: 3(x – 4) = -21

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Unit 3- Lesson 2

Aim: I can simplify negative and zero exponents.

Warm Up: Express in expanded form.

1) (-6)5 2) (3x)2 3) (2

5)3

Express in exponential form.

4) 7 ∙ 7 ∙ 7 ∙ 7 ∙ 7 5) (8)(8)(8)

Guided Practice:

Discovery to the Zero Exponent Rule

What happens when you raise a number to a zero power? Look for a pattern as you fill in the table below. Then,

evaluate each expression using what you know about dividing a number by itself.

Expression The Expression in

Expanded Form

Rewrite Using

Exponents

Evaluate

𝟓𝟔

𝟓𝟔

𝒙𝟓

𝒙𝟓

(−𝟒)𝟑

(−𝟒)𝟑

Rule: Any number raised to the ________________ power will ALWAYS be ________.

Note this works when 𝑥 ≠ 0

Exercise 1- Evaluate the following

(a) (−9821)0 (b) (4𝑥)0 (c) 4𝑥0

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Discovery to the Negative Exponent Rule

What happens when you raise a number to a negative power? Look for a pattern as you fill in the table below.

Rule:

Exercise 2- Write each expression using a positive exponent

(a) 8−5 (b) 3−9 (c) 𝑧−2 (d) 𝑝−4

Exercise 3- Evaluate each expression

(a) (−6)−2 (b) 3−3 (c) 2−4 (d) 5−3

Exercise 4- Write each fraction as an expression using a negative exponent

(a) 1

29 (b)

1

64 (c)

1

𝑒5 (d)

1

74

Expression Expanded Form Rewrite Using

Exponents

Rewrite as a

Fraction

22

25

2 ∙ 2

2 ∙ 2 ∙ 2 ∙ 2 ∙ 2

44

410

(−9)2

(−9)7

𝑎6𝑏5

𝑎9𝑏12

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Problem Set:

Simplify each expression and re-write with a positive exponent

(a) 7𝑎0𝑏3 (b)

68

69

(c) 8𝑥−2

(d) 10𝑥−4𝑦5 (e)

8𝑥9

2𝑥 (f) (

3

4)−1

(g) (4𝑥−2𝑦5𝑧−3)(5𝑥3𝑦−5𝑧−2) (h) 22(24 + 2−8) (i) −𝑥3𝑦−6

Determine the missing (?) value in each:

(a) 𝑥6

𝑥? = 𝑥4 (b)

28

2? = 29

Lesson Summary:

• Anything raised to the zero power is always __________.

• When you have negative exponents, in order to make them positive you:

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Unit 3 – Lesson 2 Homework

Using the Laws of zero and negative exponents, express the answer with positive exponents

1) 03 2) 02x 3) 0)2( x 4)

0)(4 xy

5) 0)(4 ba 6)

0)4( ab 7) 5−3 8) 12−1

9) (3x)-7 10) -8a-1b2 11) 5x0y3z-9 12) 32x4y0z-2

13) 42

48 14) 12−1 15) 3𝑥−4

18) Write an equation that can be used to find the value of x algebraically.

2x + 17

6x + 9

20) Evaluate: -3xy – x + y2 if x = 2 and y = -3

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Unit 3 – Lesson 3

Aim: I can multiply exponents with like bases.

Warm Up: What is another way you can abbreviate each expression?

(a) 3 + 3 + 3 + 3 + 3 (b) 3 ∙ 3 ∙ 3 ∙ 3 ∙ 3

Guided Practice:

Exercise 1- For each of the following expressions, name the constant, coefficient, base, variable, and exponent:

Expression Constant Coefficient Base Variable Exponent

6𝑥2 − 5

42

10𝑥3 + 1

𝑦2

Multiplying Exponents Discovery

Exercise 2- For each of the following expressions, simplify by expanding then re-write in exponential form

Expression to be simplified The expression in expanded form End result in exponential form

𝟑𝟐 ∙ 𝟑𝟒 (3 ∙ 3) ∙ (3 ∙ 3 ∙ 3 ∙ 3) 36

𝒙𝟓 ∙ 𝒙𝟑 (x ∙ x ∙ x ∙ x ∙ x) ∙ (x ∙ x ∙ x)

𝟓𝟔 ∙ 𝟓𝟒

𝒚𝟕 ∙ 𝒚𝟓

Rule: When multiplying terms with like _____________, you keep the base and _____________ the exponents.

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Problem Set: Simplify the following expressions

(1) 𝑥4 ∙ 𝑥3

(2) (1

7)6 ∙ (

1

7)2

(3) 4𝑦3 ∙ 8𝑦2

(4) 2𝑟4𝑛3 ∙ 3𝑟𝑛2

(5) 42 ∙ 410 ∙ 4−3

(6) 𝑘5 ∙ 𝑘

(7) 𝑥3(𝑥13 + 𝑦2)

(8) 27 ∙ 2 ∙ 2−3

Challenge: Can you re-write the given expression to have the same base and follow the law to multiply powers:

𝟐𝟑 ∙ 𝟒𝟐

Exit Ticket:

11

Unit 3 – Lesson 3 Homework

Find the product and express with a positive exponent.

1) 22 ∙ 25 2) 118 33 3) 44 ∙ 4 4) 6−3 ∙ 62

5) (1

2)−2∙ (1

2)1 6) 𝑥4 ∙ 𝑥0 7) 3 ∙ 3−3 ∙ 3 ∙ 30 8) (

2

3)−5∙ (2

3)9

9) (𝑥

𝑦)4∙ (𝑥

𝑦)−1

10) 7−8 ∙ 78 ∙ 7 11) 𝑦4 ∙ 𝑦9

12) Amy wrote these expressions: 63 35 102

Part A: Write these expressions in order from least to greatest. ________ ________ __________

Part B: Explain how you know your answer is correct

__________________________________________________________________________________________

__________________________________________________________________________________________

13) Which is -70 in standard form? 14) Which shows (2-2 )( 26 ) in exponential form?

a. -7 b. -1 a. 24 b. 2-4

c. 0 d. 1

7 c. 2-8 d. 2-12

15) Which of the following equations has no solution?

A) 3x + 15 = 3(x + 5) B) 3x + 7 = 2x + 7 C) 3x + 5 = 3(x+5) D) 3x + 9 = 15

Write the following in exponential form.

16) xxx 333 ___________ 17) yyyxx 55 ____________ 18) 3

7 ∙ 3

7 ∙ 3

7 ∙ 3

7 _________

Express in expanded form

19) 74 _________________ 20) (3x)3 ____________________ 21) x3y5 ______________________

Fill in the blanks about whether the number is positive or negative.

22) If n is a positive even number, then (−55)n is __________________________.

23) If n is a positive odd number, then (−72.4)n is __________________________.

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Unit 3 – Lesson 4

Aim: I can multiply monomials

Warm Up: Quick Review

Negative Exponents

Rewrite a negative exponents as a __________________ by ________________________________________

ANYTHING TO THE ZERO POWER IS EQUAL TO___________________!!!!

Multiplying Exponents

_________________________________ the coefficients

_____________________________ the base and ________________________________ the exponents

Express answers as a_______________________exponent

Guided Practice:

Multiplying Monomials

1) (-6x)(5x4) 2) (4b3)(8b2) 3) (7m4)(m3)

4) (7p5)(2p7) 5) (a3)(a2) 6) (9x5)(-5y3)

4) (5x²)(3x³) 5) (-6ab3)(-2a2b7) 6) (3ab)(-5a²bc³)

7) (2x-6y5)(-5x2y-3) 8) 7𝑥2 ∙ 3𝑦6 9) 5𝑐−3 ∙ 3𝑐9

NOTE: If there is a coefficient and exponents:

1st:_______________________________________________________________________________________

2nd:______________________________________________________________________________________

3rd : ______________________________________________________________________________________

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Problem Set:

10) 4𝑥2 ∙ 7𝑥4 ∙ 𝑥 11) 2𝑥2 ∙ 5𝑥7 12) 7𝑥−2 ∙ −3𝑦3

13) 4𝑥3 ∙ −2𝑥7 14) 9−2 ∙ 96 15) (2𝑥3)(17𝑥7)

16) 12 1010 17)

63 xx 18) 26 22

19) (3𝑥6)(4𝑥7)

(2𝑥3) 20)

5

𝑥3(−4𝑥6) 21) −5𝑥7 ∙ 13𝑥4

22) 7𝑥2 ∙ 3𝑦6 23) 5

𝑥3(3𝑥8) 24)

2

𝑥2(3𝑥7)

25) (5𝑥8)(3𝑥7)

(2𝑥3) 26) 63 ∙

6

67 27) 49 ∙ 4−6

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Unit 3 – Lesson 4 Homework

Simplify

1) (3x6)(2x4) 2) (4m8n2)(-2mn4) 3) )5)(2( 5324 yxyx

4) )8)(6( 29 xx 5) ))(3( 4364 yxyx 6) 83 xx

7) 75 99 8) 8 ∙8

85 9) 53 xx 10) 0)(4 ba

11) Which exponential expression is equivalent to 45(4-8)?

A) 413 B) 43 C) 1

43 D)

1

4−3

12) Which number is equivalent to 36(3-4)?

A) 3 B) 9 C) 27 D) 1

9

13) If the length of a rectangle is represented by 4x2 and the width is 7x7, which expression

represents the area of the rectangle?

A) 11x9 B) 11x14 C) 28x9 D) 28x5

14) Solve: 1

6𝑥 + 5 =

1

3(𝑥 + 9) (no calculator)

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Unit 3- Lesson 5

Aim: I can use the distribute property with exponents.

Warm Up:

1) 2(x + 8) 2) 4(6x – 7) 3) - (4x2 – 1) 4) -7(2x2 – 8)

Guided Practice:

Using the Distributive Property:

Rule:

Step 1: Multiply Coefficients

Step 2: Add Exponents of like bases

Examples:

1) x(3x + 4) 2) x(2x2 – 9)

3) - x4(6x3 – 8x2) 4) - x5(7x4 – 2x3)

5) 4x7(2x5 – 3x3 + 8x) 6) 5x3(x4 – 2x3 + 3x)

7) x5y2(2x4 – 6xy + y2) 8) 4x2y4(3x5 – 2xy – 5y2)

*9) (x + 8)( 2x2 + 5x + 3)

16

Problem Set:

1) 3(4x +7) 2) )45(3 2 x

3) )59( 25 xxx 4) )4712(2 4563 xxxx

Exit Ticket:

17

Unit 3 Lesson 5- Homework

Review: Multiplying a Monomial by a Monomial. Write as a positive exponent if necessary.

1) (x6)(x-3) 2) (5x-3)(3x-4) 3) (9x-4y-3)(4x-3y6) 4) (2x-5y3)(3x4y-8)

Multiplying a Monomial by a Polynomial

5) -6(2x2 + 3) 6) x(x2 – 7x) 7) -2x4(3x5 – 2x3) 8) 5x2(4x3 + 5x2 + 10x)

9) -3c5(7c3 – c2) 10) 3h(5h3 – 6h) 11) 2x(3x3 - x2 – 5) 12) -2n (3n2 – 3n – 7)

13) w2 (5w3 + 7w – 3) 14) 6a3b3(2a5 – ab + 2b4) *15) (x + 2)( 5x2 + 3x + 8)

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Unit 3 – Lesson 6

Aim: I can simplify an exponential expression raised to a power.

Warm Up: Simplify the following.

1) -2x4(3x5 – 2x3)

2) (5x-3)(3x-4)

Discovering the Laws of Exponents: Power to a Power Rule

What happens when you raise a power to a power? Look for a pattern as you fill in the table below.

Example Write in Expanded Form Rewrite using Exponents

(23)2

(32)4

(54)3

(72)2

[ (1

2)2 ]5

Rule: When you raise a power to a power, keep the ______________ and _________________ the exponents.

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Discovering the Laws of Exponents: Product to a Power Rule

What happens when you raise a product to a power? Look for a pattern as you fill in the table below.

Example Write in Expanded Form Rewrite using Exponents

(2 ∙ 3)3

(2 ∙ 3) ∙ (2 ∙ 3) ∙ (2 ∙ 3) 2 ∙ 2 ∙ 2 ∙ 3 ∙ 3 ∙ 3

2333

(4 ∙ 6)5

(6𝑎)4

(7 ∙ 4 ∙ 11)2

Rule: When finding a product raised to a power, you find the power of each factor and then ______________

Problem Set:

Simplify the following expressions, do not evaluate. Rewrite as positive exponents if necessary.

(1) (52)3 (2) (𝑥5)4 (3) (𝑦4)−3 (4) (62)2 ∙ 6−5

(5) (73)4 (6) (2−1)0 (7) (−27)2 ∙ (−2)−1 (8) (-3𝑦5)2

(9) (2𝑥3𝑦−2𝑧4)3 (10) (6−2)3 (11) (𝑥4 ∙ 𝑥2)2 (12) (2𝑎3𝑏−2)3

(13) The formula for the volume of a rectangular prism is 𝑉 = 𝐿𝑊𝐻. If the length is 84, the width is 8−2, and

the height is 80. Express the volume, in exponential form.

20

Unit 3 -Lesson 6 Homework

Simplify using the laws of exponents. Express as a positive exponent (Do not compute)

1) (84)3 = ______ 2) (21)0 = ______ 4) (72)2 = ______ 5) (810)2 = _____

6) (37)3 ∙ (32)4 = ______ 7) (90)6 = ______ 8)[(1

2)3

]2

= ______ 9) (124)4 = _____

10) 62 99

11) (𝑦15)2 = ______ 12) (3𝑥5)4 = ______ 13) (3𝑦3 ∙ −2𝑦)3 = ______ 14) (5𝑥7)2

15) Which is (-7)2 in standard form? 16) What is the value of (3-2) ?

a. -49 b. −1

49 a. -9 b. 9

c. 49 d. 1

49 c. −

1

9 d.

1

9

17) In exponential form, what is the area of a square that has length of 43 ?

18) Determine the missing (?) value in each:

a) (5?)3 = 512 b) 28

2? = 29 c) (−2𝑚3𝑛4)? = −8𝑚9𝑛12

19) The formula for the volume of a rectangular prism is V = LWH. If the L = 84 and W = 8−2

and the H = 80. What is the volume in exponential form?

20) The formula for the volume of a cube is V = s 3 where s is the length of the side of the square. Express the

volume of a cube in simplest terms of x whose side is 6x 8 .

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Unit 3 – Lesson 7

Aim: I can divide like bases with exponents.

Warm up:

1. What does 53 represent?

2. What does ( 1

3)2 represent?

3. What does (-6)4 represent?

Guided Practice:

Dividing Exponents Discovery

Exercise 1- For each of the following expressions, simplify by expanding then re-write in exponential form

Expression to be simplified The expression in expanded form End result in exponential form

𝟓𝟔

𝟓𝟐

5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5

5 ∙ 5

54

𝒙𝟓

𝒙𝟐

x ∙ x ∙ x ∙ x ∙ x

x ∙ x

𝟒𝟐

𝟒𝟑

𝒙𝟕𝒚𝟏𝟎

𝒙𝟒𝒚𝟔

Rule: When dividing terms with like _____________, you keep the base and _____________ the exponents.

Problem Set: Simplify the following expressions

(1) 𝑥5𝑦4

𝑥2𝑦 (2)

510

52 (3)

68

6

22

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

_______________________________________________________________________________________

(4) 𝑥6𝑦8

𝑥4 (5)

𝑎6𝑏

𝑎4𝑏 (6)

59

26

(7) 8𝑎9𝑏5

12𝑎3𝑏4 (8)

816∙85

812 (9)

𝑎4𝑏𝑐6

𝑎4𝑏𝑐5

(10) 6𝑚5𝑛4

2𝑚2𝑛4

11. Bryan and Brendan simplify the following expression 𝑚3

𝑚7, below are their responses.

Bryan: 𝑚4 Brendan: 𝑚−4

Determine which student got the correct answer and explain the mistake made by the other student.

Exit Ticket:

23

Unit 3- Lesson 7 Homework

Simplify using the laws of exponents. Express all answers as a positive exponent.

1) 911

99 2)

710

79 3)

104

10−9 4)

46

43

5) 𝑥3

𝑥 6)

79

53 7)

𝑥4𝑦7

𝑥2𝑦3 8)

𝑤4𝑦12

𝑥7𝑦3

11) 99

95 12)

(2

5)7

(2

5)2 13)

𝑥15

𝑥3 14)

𝑥5

𝑥−2

15) 𝑥15𝑦3

𝑥5 16)

25

2−9 17)

𝑥4

𝑥−5 18)

(1

3)9

(1

3)2 19)

2−4

2−7

20) Determine the missing (?) value in each:

a) 𝑥

𝑥?

6 = 𝑥4 b)

28

2? = 29 c)

𝒙?

𝒙𝟓= 𝒙𝟕

21) Solve: 2

5𝑥 − 8 = 2 (no calculator)

24

Unit 3- Lesson 8

Aim: I can divide a polynomial by a monomial

Warm Up:

Simplify and write each answer with a positive exponent

1) x10 ÷ x4 2) 710

79 3)

104

10−9 4)

46

43

Guided Practice:

Dividing a Polynomial by a Monomial

Is 12+6

2 the same as

12

2+6

2? Justify your answer.

How can we rewrite 15+5

5 as two separate fractions?

How can we rewrite the given fractions as separate fractions?

1) 32m − 20

4 2)

6x+2

2 3)

12𝑛4− 6𝑛3+ 24𝑛2

6𝑛

4) 20𝑛4− 15𝑛3+ 35𝑛2

5𝑛2 5)

15𝑥2− 3𝑥

3𝑥

6) (22𝑥8 − 18𝑥6 + 10𝑥3) ÷ 2𝑥3 7) (5𝑥4 + 25𝑥3 − 10𝑥2) ÷ 5𝑥

25

Problem Set:

8) a5 ÷ a3 9) -27x9 ÷ -3x 10) -40a2 ÷ 5a2

11) (45m – 27) ÷ 9 12) (30n3 – 24n2 + 18n) ÷ 6n

13) 2

6

x

x 14)

34 xx 15) 3

9

5

15

x

x

16) 210 824 xx 17) 5

2

6

18

x

x 18)

10

2030 x

19) x

xxx

3

3129 53 20)

3

346

6

6186

x

xxx 21)

3

789

2

284

x

xxx

26

Unit 3- Lesson 9

Multiplying Monomials

1.________________________________________________________________________________________

2.________________________________________________________________________________________

3.________________________________________________________________________________________

1. 9-5(92) 2. -2x • x5 3. (5x2y)(4xy2) 4. (2x)(5x) 5. (3x2)(4x4) 6. (x3)(4x2) (-x3)

Power to a Power

1.________________________________________________________________________________________

2.________________________________________________________________________________________

7. (32)3 8. (a4c3)5 9. (4n2)2 10. (-3xy)2 11. (5n2)2 12. (3xy4)2

Dividing Exponents

1.________________________________________________________________________________________

2.________________________________________________________________________________________

3.________________________________________________________________________________________

13. 5

8

7

7 14.

9

4

x

x 15.

x

x

3

15 7

16. 93

39

25

20

yx

yx 17.

8

8

x

x 18.

5

10

18

9

x

x 19.

257

14

yx

xy

Zero Exponents ________________________________________________________________________

20. 50 21. 4x0 22. (8x)0 23. 3xy0 24. x-6(x6) 25. 5

5

x

x 26. 7(ab)0

Negative Exponents_______________________________________________________________

27. 4-3 28. 5x-2 29. -9x-4 30. 18x-5y3

27

Simplify. Rewrite all answers in positive exponential form.

1. 35 44 2. 28 99 3. )12()12( 6 4. 85 33

5. 85 88 6. 05 77 7. 2119 444 8. 62 )15()15()15(

9. 35 34 xx 10. 42 26 yy 11. 38 86 mm 12. )2)(12( 235 acca

13. 32 )4( 14.

57 )5( 15. 62 )3(

16. 43 )6(

17. 12 )8( 18.

02 )4( 19. 32 )3( x 20.

35 )2( y

21. 352 )24( 22.

253 )57( 23. 623 )43(

24. 350 )89(

25. 57 26.

09 27. 32 28. x3(x-5)

29. 0)2( 30.

35 )2( x

28

Simplify using the laws of exponents. Rewrite as a positive exponent if necessary.

31) 911

99 = ______ 32)

710

79 = ______ 33)

104

109 = ______ 34)

46

413 = ______

35) 𝑥3

𝑥 = ______ 36)

𝑚2

𝑚3 = ______ 37) 𝑥4𝑦7

𝑥2𝑦3 = ______ 38)

𝑤4𝑦12

𝑥7𝑦3 = ____

39) 15𝑥3

5𝑥2 = ______ 40)

12𝑥5

−6𝑥2 = ______ 41)

14𝑥11

21𝑥2 = ______ 42) −18𝑥

9

2𝑥14 = ______

43) Mario wrote the expression 9-2.

Part A: What is the value of the expression?

Part B: Is the expression (-9)2 equivalent to 9-2? Explain how you know.

44) Sarah wrote that (35)7 = 312. Correct her mistake. Write an exponential expression using a base of 3 and

exponents of 5, 7, that would make her answer correct.

45) Determine whether the simplified answer would be positive or negative.

a) (−47)𝑛 if 𝑛 is a positive even number. b) (−8.663)𝑛 if 𝑛 is a positive odd number.

46) Josie says that (−15) × ⋯× (−15)⏟ 6 𝑡𝑖𝑚𝑒𝑠

= −156. Is she correct? How do you know?

47) Write an exponential expression with (−1) as its base that will produce a positive product.

48) What is the value of 74 33 ?

A. 1

−27 B.

1

27 C. -27 D. 27

49) The result of 8−4 comes from which expression?

A. 8−2 ∙ 82 B. 168 ÷ 24 C. 83 ∙ 8−7 D. 8−4 ∙ 8

50) The formula for area of a square is A = s2 . If the side of the square is 7x6, what would be the area in terms

of x?

29

In order to find the answer to the question below complete each of the problems below. Then find the answer on a ghost

hanging in the room. Put the letter that is on the ghost with the correct answer in the box with the problem that you solved.

Unit 3 REVIEW SHEET

Simplify

45(48) Simplify

(4x2)0

Simplify

(-2x4)3

Simplify and

express with a

positive exponent

(4x7)(-3x-9)

Simplify 18𝑥7

3𝑥2

Simplify

5𝑥7

15𝑥7

Simplify and express

with a positive

exponent

33

38

(x-6)2

Simplify and

express with a

positive exponent

3x-5

Simplify and

express as a

positive exponent

574−255

5−347

Simplify

8x0y5

3

4

x

x

76

78

-4x3(3xy2)

Simplify

12x2+ 6x

3x

12𝑥8

2𝑥10

Compute

80+ 42

42+ 5−2

2𝑥3𝑦−3

3𝑥𝑦

)2)(6( 235 acca

30

Unit 3: 1) Write in expanded form 2) Write the following in exponential form.

a. 53𝑥2 b. (3

4𝑦)

4

a. 2

3 ∙

2

3 ∙

2

3 ∙

2

3 b. 5 ∙ 5 ∙ 5 ∙ 5 ∙ 5 ∙ 𝑎 ∙ 𝑎 ∙ 𝑎

________________ _______________ _____________ ______________

3) Write the following as POSITIVE exponents 4) Compute the value (evaluate)

a. 5−3 b. 𝑥−1

9−5 c. (

2

3)−2

a. (−2)4 b. (4

7)2

c. 52 − 34 + 70

______ _ _______ _______ _______ _______ _______

5) Multiply. Exponents must be put into positive exponential form

a. 8−3 ∙ 87 = ______ b. 44 ∙ 413 ∙ 4 = ______ c. 3𝑥6 ∙ −6𝑥19 = ______ d. 3−5 ∙ 3−9 = ______

6) Raising a Power to a Power: Multiply and put answers into positive exponential form.

a. (54)3 = ______ b. (3𝑥−2𝑦)4 = ______ c. (7−8)2 ∙ 74 = ______ d. (−2𝑥9)2 = ______

7) Dividing exponents with the same base. Put answers in positive exponential form.

a. 614

65 = ______ b.

𝑥4

𝑥7 = ______ c.

12𝑦11

−8𝑦9 = ______ d.

9𝑥4𝑦8𝑧

3𝑥2𝑦8𝑧4 = ______

e. 35 ÷ 33 = _______ b. 87 ÷ 813 = _______ c. 12𝑥11 ÷ 4𝑥3 = _______ d. (−2)5

(−2)5 = _______

8) What is the value of the expression (79

74) ∙ 7−2

31

Unit 1: 9) Perform the indicated operations and evaluate 10) Given a = -2 ; b = 3 and c = -1, evaluate the

following

a. 72 − (−2)4 b. 1

2 ÷

3

4+

2

3 a. 𝑐(𝑎 + 𝑏) b.

𝑎3+𝑐

𝑏

11) Simplify each expression

a. 3

5 (5𝑥 − 15) b. 5x + 6 – 3x + 8 c. 5(2y – 11) – 6y d. 4 – 2(4x + 3)

12) Given the rectangle below:

a. Express the area of the rectangle. b. If you put a fence around the rectangle

in simplest terms of x. how much fence would you need?

3x – 2

13a). If the temperature rises from -9 degrees 13b) While on a diet, Bill’s weight started at 173 lb. He gained

to 17 degrees, how much did it increase? 4 lb the first week, lost 8 lb the 2nd week and gained 2 lb

the 3rd week. How much does he now weigh?

14) Using the equations to the right, determine the following: 𝐶 = 5

9(𝐹 − 32) 𝐹 =

9

5𝐶 + 32

a. If C = 10, find F. b. If F = 68, find C.

15) Determine if the following is a monomial, binomial or trinomial

a. 3𝑥 − 7𝑦 _______________ b. 9𝑥5𝑦 _______________ c. 9 − 3𝑥 + 7 _______________

𝟓

32

Unit 2:

Solve the following equation for the missing variable, otherwise determine no solution or infinitely many solutions

16) 4x - 13 = -9 17) 0.8 - 2x = 7.6 18 ) 4

5𝑥 − 3 = 9

19) 3x + 12 = 3(4 + x) 20) -3(2x – 1) = 3x + x + 53

21) 6(2𝑥 − 8) = 12(𝑥 + 3)

22) 3

5+

1

4𝑥 =

1

2 23) 0.9x – 4 = 3x + 2.3 24) 4x + 7 = 12 – 5

25) What is the value of 54 × 5-6? 26) Which number is irrational?

A. –25 B. 1

25 C. −

1

25 D. 25 A. −

4

3 B. √49 C. 16.12537… D. 0. 64̅̅ ̅̅̅

27) Write an equation that can be used to solve the following problem. Justin has $500 in his bank account and

wants to deposit $20 per month. In how many months, m, will he have $3,480?

28) Which expression represents 4 less than twice a number, n ?

A. 4 – n B. n - 4 C. 4 - 2n D. 2n - 4

29) What is the value of 12 + 2(12 - 9)2?

A. 24 B. 30 C. 84 D. 126