8 exponents - highpeakmrsmith7th8thgrademathematics.weebly.com/uploads/1/... · lesson 8-1 problem...

Name ________________________________________ Date __________________ Class __________________

Practice 8-1 Exponents

Write in exponential form.

1. 6 • 6 • 6 • 6 • 6 • 6 2. 7 • 7 • 7 • 7

________________________________________ ________________________________________

3. (8) • (8) • (8) • (8) 4. 5 • 5 • 5 • b • b • b • b

________________________________________ ________________________________________

Simplify.

5. 102 6. (6)2 7. 82 8. (7)2

9. (5)3 10. 122 11. (9)2 12. (4)3

13. 25 14. 54 15. (3)4 16. 63

17. (10)2 18. 73 19. (14)2 20. (16)2

Evaluate each expression for the given values of the variables.

21. n3 5 for n 4 22. 4x2 y3 for x 5 and y 2

23. mp q2 for m 5, p 2, and q 4 24. a4 2(b c2) for a 2, b 4, and c 1

Chapter

8

Name ________________________________________ Date __________________ Class __________________

25. n3 5p for n 4 and p 3 26. x2 y3 for x 5 and y 3

27. ab 6c for a 3, b 4, and c 2 28. s4 (t r)5 for s 2, t 7, and r 8

29. yx xy xy for x 2 and y 3 30. 5x9 (y z) for x 1, y 10, and z 6

31. xz yx for x 2, y 4, and z 5 32. ac bc for a 12, b 6, and c 2

33. Write an expression for five times a number used as a factor three times.

Name ________________________________________ Date __________________ Class __________________

Practice 8-2 Integer Exponents

Simplify.

1. 101 2. 106 3. 102 4. 101

5. 100 6. 103 7. 105 8. 106

9. 107 10. 104 11. 103 12. 105

Simplify.

13. (2)3 14. 34 15. (4)2 16. 24

17. 52 18. 63 19. (9)2 20. (3)3

21. 8 30 21 22. 4 (6)0 41

Chapter

8

Name ________________________________________ Date __________________ Class __________________

Original content Copyright © by Holt, Rinehart and Winston. Additions and changes to the original content are the responsibility of the instructor.

14 Holt Mathematics

23. 3(9)0 42 24. 6 (5)2 (4 3)0

25. One centimeter equals 102 meter. Simplify 102.

26. The area of a square is 104 square feet. Simplify 104.

Name ________________________________________ Date __________________ Class __________________

Practice 8-2B Integer Exponents

Simplify.

1. 103 2. 105 3. 104 4. 102

5. 101 6. 106 7. 102 8. 103

9. 10 10. 105 11. 102 12. 106

Simplify.

13. (3)4 14. 53 15. (6)3 16. 43

17. 43 18. 32 19. (6)3 20. (2)2

Chapter

8

Name ________________________________________ Date __________________ Class __________________

21. 6 60 22 22. 6 (19)0 23

23. 2(4)0 24 24. 4 (3)2 (2 4)0

Name ________________________________________ Date __________________ Class __________________

Lesson 8-1 Problem Solving Exponents

Write the correct answer.

1. The formula for the volume of a cube is V e3 where e is the length of a side of the cube. Find the volume of a cube with side length 6 cm.

Solution:

V e 3, e 6

V 63 6 • 6 • 6 216

216 cm3

3. The surface area of a cube can be found using the formula S 6e2 where e is the length of a side of the cube. Find the surface area of a cube with side length 6 cm.

________________________________________

2. The distance in feet traveled by a falling object is given by the formula d 16t2 where t is the time in seconds. Find the distance an object falls in 4 seconds.

d 16t2

d 16 _____2

d _____

________________________________________

4. John is paid 2 cents for doing the dishes the first night, 4 cents the second, 8 cents the third, and so on, doubling each night. Write an expression using exponents for the amount John will get paid on the tenth night.

________________________________________

Use the table below for Exercises 5–7. It shows the number of e-mails forwarded at each level if each person continues a chain by forwarding an e-mail to 10 friends. Choose the letter for the best answer.

5. How many e-mails were forwarded at level 5 alone?

6. How many e-mails were forwarded at level 6 alone?

7. How many total e-mails have been forwarded after 6 levels?

Forwarded E-mails Level E-mails forwarded

1 10 2 100 3 1,000 4 10,000

Chapter

8

Name ________________________________________ Date __________________ Class __________________

Lesson 8-2 Problem Solving Integer Exponents


1. The weight of 107 dust particles is 1 gram. Simplify 107.

3.As of 2001, only 106 rural homes in the United States had broadband Internet access. Simplify 106.

2. The weight of one dust particle is 107 gram. Simplify 107.

4.Atomic clocks measure time in microseconds. A microsecond is 106 second. Simplify 106.

5. The diameter of the nucleus of an atom is about 1015 meter. Simplify 1015.

7. A ruby-throated hummingbird weighs about 32 ounce. Simplify 32.

6. The diameter of the nucleus of an atom is 0.000001 nanometer. How many nanometers is the diameter of the nucleus of an atom?

8. A ruby-throated hummingbird breathes 2 53 times per minute while at rest. Simplify this amount.

Chapter

8

Practice 8-3 Properties of Exponents

Write the product or quotient as one power.

1. x 10 • x 8 2. (10)14 • (10)4 3. d5

d 4. 92 910

5. t 12 • t 5 6.

(x)10

(x)8 7. 168 168 8. 149 • 149

9. (k)12 (k)9 10. 15 • 1511 11. 1710 • 17 12. x 8 x 8

13. y12 • y10 14. 159 • 1514 15. (11)20 • (11)10 16. (a)6 • (a)7

17.

1719

172 18.

1413

1415 19.

2317

239 20.

(a)12

(a)7

Simplify.

21. (53)4 22. (74)2 23. (26)1 24. (x2)5

25. (32)3 26. (120)2 27. (w4)2 28. (y1)6

29. (92)3 30. (100)3 31. (x4)2 32. (52)0

Chapter

8

Write as one power.

33. x 3 • x 2 • x 4 34. 55 52 • 53 35. 84 • 8 82

36. x 7 x 2 x 3 37. (4)4 • (4)6 (4)2 38. 25 2 • 22 23

39. Justine and ninety-nine of her co-workers won the lottery worth $108. They all received their winnings over ten years. How much did each receive in a one-year period?

40. A number to the 7th power divided by the same number to the 3rd power equals 256. What is the number?

41. Jefferson High School has a student body of 64 students. Each class has approximately 62 students. How many classes does the school have? Write the answer as one power.

42. Write the expression for a number used as a factor fifteen times being multiplied by a number used as a factor ten times. Then, write the product as one power.

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Worksheet by Kuta Software LLC

EJMS Math

Practice 8-3B

Name___________________________________ ID: 1

Date________________ Period____

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-1-

Use shortcuts to simplify. Your answer should contain only positive exponents.

1) 8 × 82 2) 6 × 6

3

3) 3 × 33 4) 7 × 7

4

5) 2p2 × 4p 6) 2v2

× 3v

7) 2x × 2x2 8) 3aa2

9) 3

33 10)

22

24

11) 5

4

512)

43

43

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13) 8b2

5b214)

6n3

n4

15) 2n4

4n316)

2v2

8v3

17) 32 18) 22

19) (22)220) (32)2

21) (3a)2 22) n2

23) (a2)2 24) (2n)2

Practice 8-4 Scientific Notation

Write each number in standard notation.

1. 2.54 102 2. 6.7 102 3. 1.14 103 4. 3.8 101

5. 7.53 103 6. 5.6 104 7. 9.1 105 8. 6.08 104

9. 8.59 105 10. 3.331 106 11. 7.21 103 12. 5.88 104

13. 8.235 107 14. 6.0089 108 15. 5.2 109

16. 2.0547 109 17. 8.394 107 18. 9.688 1011

Chapter

8

Write each number in scientific notation.

19. 75,000,000 20. 208 21. 907,100

22. 56 23. 0.093 24. 0.00006

25. 0.00852 26. 0.0505 27. 0.003007

28. 97,406,000,000 29. 0.000000000067 30. 5,280,000,000

31. 0.000000084 32. 652,100,000,000 33. 0.0000000007254

34. Jupiter is about 778,120,000 kilometers from the Sun. Write this number in scientific notation.

35. The E. coli bacterium is about 5 107 meters wide. A hair is about 1.7 105 meters wide. Which is wider, the bacterium or the hair?

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EJMS Mathematics

Practice 8-4B

Name___________________________________ ID: 1

Date________________ Period____

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Write each number in scientific notation.

1) 0.028 2) 0.8

3) 0.009 4) 8000

5) 60 ´ 105 6) 0.054

7) 0.88 8) 260000

9) 0.4 10) 5700

11) 1240000 12) 0.00000015

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Write each number in standard notation.

13) 2.3 ´ 10-3 14) 5 ´ 10

1

15) 4.1 ´ 10-1 16) 2.1 ´ 10

2

17) 8.9 ´ 10-3 18) 6.5 ´ 10

-6

19) 8.8 ´ 10-5 20) 5.1 ´ 10

5

21) 6 ´ 10-6 22) 4.9 ´ 10

-8

23) 8.8 ´ 10-2 24) 2.68 ´ 10

6

Name ________________________________________ Date __________________ Class __________________

Lesson 8-3 Problem Solving Properties of Exponents

Write each answer as a power.

1. Cindy estimates that there are 210 fruit flies in each of 22 jars. How many fruit flies are there in all?

3.A satellite orbits the earth at about 134 km per hour. How long would it take to complete 24 orbits, which is a distance of about 135 km?

2. If an antibiotic kills bacteria at a rate of 89 per sec, how many bacteria would be killed after 82 sec?

4. The side of a cube is 34 centimeters

long. What is the volume of the cube? (Hint: V s3.)

Use the table to answer Exercises 56. The table describes the number of people involved at each level of a pyramid scheme. In a pyramid scheme, each individual recruits others to participate, who in turn recruit others, and so on. Choose the letter of the best answer.

5. Using exponents, how many people will be involved at level 6?

6. How many times as many people will be involved at level 6 than at level 2?

Pyramid Scheme Each person recruits 5 others.

Level Total Number of People

1 5

2 52

3 53

4 54

Chapter

8

Name ________________________________________ Date __________________ Class __________________

Lesson 8-4 Problem Solving Scientific Notation


1. A new transistor can switch on and off 1.5 trillion times a second. Express the speed of the transistor in scientific notation.

3. The length of an element in the transistor is 2 105 times smaller than the width of a human hair. Express 2 105 in standard notation.

2. With this transistor, computers will be able to do 1 109 calculations in the time it takes to blink your eye. Express the number of calculations using standard notation. (Hint: Write 9 zeros)

Use the table to answer Exercises 5–9. Choose the best answer.

4. Express a light-year in miles using scientific notation.

5. How many miles is it from Earth to the star Sirius?

6. How many miles is it from Earth to the star Canopus?

Distance From Earth To Stars Light-Year 5,880,000,000,000 mi

7. How many miles is it from Earth to the star Alpha Centauri?

Chapter

9

Star Constellation Distance

(light-years)

Sirius Canis Major 8

Canopus Carina 650

Alpha Centauri Cantaurus 4

Vega Lyra 23

Practice 8-5 Squares and Square Roots

Find the two square roots of each number.

1. 49 2. 36 3. 121 4. 225

5. 9 6. 100 7. 64 8. 625

9. 225 10. 576 11. 361 12. 625

13. 400 14. 729 15. 1024 16. 2500

Simplify each expression.

17. 2 64 10 18.

196

49 19.

100

25 20. 73 48

21. 3217 22. 100 19 23. 100 25 24.

25

4

1

2

25. 12116 26. 6436 27. 36 36 28. 3( 144 6 )

Chapter

8

29.

81

324 30. 196 49 31. 6( 225 9) 32. ( 144 64 )

33. The distance from base to base, home plate included, on a baseball field is 90 ft. The bases form a square. What is its area?

Switzerland’s flag is a square, unlike other flags that are rectangular.

34. Suppose a seamstress is making a flag that has to have an area less than 50 square meters. What is the longest length, to the nearest tenth, the sides can be?

(Hint: s A )

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EJMS Mathematics

Practice 8-6

Name___________________________________ ID: 1

Date________________ Period____

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Estimate each square root.

1) 118 2) 39

3) 31 4) 43

5) 2 6) 28

7) 64 8) 67

9) 79 10) 138

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11) 105 12) 58

13) 86 14) 44

15) 61 16) 4

17) 65 18) 97

19) 68 20) 3

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EJMS Mathematics

Practice 8-6B

Name___________________________________ ID: 1

Date________________ Period____

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Estimate each square root. Show work.

1) 123 2) 34

3) 120 4) 110

5) 114 6) 142

7) 126 8) 78

9) 50 10) 20

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11) 116 12) 109

13) 60 14) 91

15) 129 16) 64

17) 2 18) 96

19) 136 20) 10

Name ________________________________________ Date __________________ Class __________________

Lesson 8-5 Problem Solving Squares and Square Roots


1. For college wrestling competitions, the NCAA requires that the wrestling mat be a square with an area of 1764 square feet. What is the length of each side of the wrestling mat?

3. The Japanese art of origami requires folding square pieces of paper. Elena begins with a large sheet of square paper that is 169 square inches. How many squares can she cut out of the paper that are 4 inches on each side?

2. For high school wrestling competitions, the wrestling mat must be a square with an area of 1444 square feet. What is the length of each side of the wrestling mat?

4. When the James family moved into a new house they had a square area rug that was 132 square feet. In their new house, there are three bedrooms. Bedroom one is 11 feet by 11 feet. Bedroom two is 10 feet by 12 feet and bedroom three is 13 feet by 13 feet. In which bedroom will the rug fit?

5. A square picture frame measures 36 inches on each side. The actual wood trim is 2 inches wide. The photograph in the frame is surrounded by a bronze mat that measures 5 inches. What is the maximum area of the photograph?

7. A can of paint claims that one can will cover 400 square feet. If you painted a square with the can of paint, how long would it be on each side?

6. To create a square patchwork quilt wall hanging, square pieces of material are sewn together to form a larger square. Which is the least number of smaller squares that can be used to create a square patchwork quilt wall hanging?

8. A box of tile contains 12 square tiles. If you tile the largest possible square area using whole tiles, how many tiles will you have left from the box?

Chapter

8

Name ________________________________________ Date __________________ Class __________________

Lesson 8-6 Problem Solving Estimating Square Roots

The distance to the horizon can be found using the formula d 112.88 h where d is the distance in kilometers and h is the number of kilometers from the ground. Round your answer to the nearest kilometer.

1. How far is it to the horizon when you are standing on the top of Mt. Everest, a height of 8.85 km?

3. How far is it to the horizon if you are standing on the ground and your eyes are 2 m above the ground?

2. Find the distance to the horizon from the top of Mt. McKinley, Alaska, a height of 6.194 km.

4. Mauna Kea Hawaii is about 4 km tall. You should be able to see the top of Mauna Kea when you are how far away?

You can find the approximate speed of a vehicle that leaves

skid marks before it stops. The formulas S 5.5 0.7L and

S 5.5 0.8L , where S is the speed in miles per hour and L is the length of the skid marks in feet, will give the minimum and maximum speeds that the vehicle was traveling before the brakes were applied. Round to the nearest mile per hour.

5. A vehicle leaves a skid mark of 40 feet before stopping. What was the approximate speed of the vehicle before it stopped?

6. A vehicle leaves a skid mark of 200 feet before stopping. What was the approximate speed of the vehicle before it stopped?

Chapter

8

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EJMS Mathematics

Practice 8-7

Name___________________________________ ID: 1

Date________________ Period____

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-1-

Simplify each radical, if possible.

1) 82 2) 116

3) 49 4) 39

5) 141 6) 5

7) 124 8) 136

9) 34 10) 73

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11) 117 12) 45

13) 110 14) 27

15) 12 16) 43

17) 76 18) 80

19) 108 20) 53

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EJMS Mathematics

Practice 8-7B

Name___________________________________ ID: 1

Date________________ Period____

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-1-

Simplify each radical, if possible.

1) 106 2) 103

3) 14 4) 121

5) 90 6) 127

7) 6 8) 42

9) 131 10) 68

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11) 44 12) 84

13) 149 14) 33

15) 97 16) 60

17) 88 18) 9

19) 140 20) 120

8 5 18 3 2

12 3

7 4

SSimplifying Radicals Maze Name___________________________

320

162

18

432

112

8

20

108

125

63

98

14

28

81

300

726

12

75

15

27

8

27

45

70

72

18

196

30

16

85

start

��

2 10

6 3

5 5

9 7

2 7

2 7

30 10

1 1 6

2 3

4 3

9

2 2 4 2

3 4

3 5

3 8

3 2 14

3 10 4

4 20 2 5 7 2 15

9 2 3 6 9 3 3

2 3 25 10 3 3 2

3 7 7 3 8 5 3 3

4 7 7 2 2 7 3 15

2 2 14 5 3 7 10

8 exponents - highpeakmrsmith7th8thgrademathematics.weebly.com/uploads/1/... · lesson 8-1 problem...

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