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Answer Page Back to Lesson 8-1 Name 8-1B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. USES Objective H 1. An art-supply store sells tubes of white paint in 4 sizes and in 3 different brands. How many different choices of size/brand are possible? 2. Edward wears jeans, a T-shirt, and a sweatshirt every day to school. He has 6 pair of jeans, 9 T-shirts, and 4 sweatshirts. How many different outfits can he wear? 3. Amy, Beth, Carlo, and Dion plan to run for the positions of president, vice-president, secretary, and treasurer of the student council. How many ways could the four offices be filled? 4. A combination lock has 50 numbers. The combination consists of 3 numbers, each of which can repeat. How many different combinations can be formed? a. Write your answer in exponential form. b. Write your answer in base 10. 5. Emma can choose from 50 types of freshwater fish for her new aquarium. She can also choose from 12 types of artificial plants. a. If she chooses just one type of plant and one type of fish, how many different ways can she set up her tank? b. Write your answer in scientific notation. 6. A math quiz has 8 true-false questions and 17 multiple-choice questions with 4 answer choices. b. What is the probability of getting all the answers on the quiz correct by guessing? Use this information for 7–9. Seven Chicago Bears football fans each wrote a letter from the phrase “GO BEARS” on their chests to show their team support. When they arrived at the game they sat next to each other in random order. 7. How many different forms of the phrase are possible? 8. Write your answer in scientific notation. 9. What is the probability that the fans spelled the phrase correctly when they first sat down at the game? 392 Algebra Copyright © Wright Group/McGraw-Hill a. How many different answer sheets are possible? Back to Lesson 8-1 Answer Page Name 8-1B page 2 A bakery offers the following breakfast options. Doughnuts Bagels Muffins Beverages Plain Cinnamon/raisin Blueberry Orange juice Chocolate Blueberry Apple Coffee Pumpkin Oatmeal Chocolate Tea Cinnamon Apple juice Buttermilk Banana/nut 10. Gilbert always orders a bagel and a drink. How many different choices are available? 11. Before Anna gets to school she orders one item to eat and one item to drink. How many different choices can she make? Your aunt orders 1 doughnut, 2 bagels, 2 muffins, and 5 drinks for her and some co-workers. 12. Write the number of ways she can order a. in exponential form. b. in base 10. c. in scientific notation. Avery and his friends attend the Fall Frolic every year. There are 15 food booths, 20 game booths, 12 rides, and a haunted house. 13. Avery plans to eat some food and play some games. How many different choices can he make? Copyright © Wright Group/McGraw-Hill 14. Avery’s friend Melody wants to attend one food booth, one game booth, one ride and the haunted house. How many different choices does she have? 15. How does the answer to Question 14 change if Melody wants to attend 2 food booths, 2 game booths, 2 rides, and the haunted house? She can attend the same booth or ride more than once. 16. Avery’s parents also attend the festival and intend to eat at a food booth. What is the probability that they will eat at the same food booth as Avery? Algebra 393 Back to Lesson 8-2 Answer Page Name 8-2B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objective A In 1–4, an expression is given. a. Write the expression in expanded form. b. Write the expression as a single power. 1. 53 · 5 2. x 3 · x 2 a. a. b. b. 3. (−34)2 4. (x 3)5 a. a. b. b. In 5–25, simplify. 5. a5 · a 6. b2 · b4 7. c7 · −1c 3 8. 2d · 5d 9 9. e 3f 4 · e 2f 10. jk · 3jk2 Copyright © Wright Group/McGraw-Hill 11. −2m2n3 · −4m4n5 12. (6p0)3 13. 2q(q 3)4 14. 5(rs)2 15. 3t 0(t 5)5 16. b20 · b5 17. −u24 · uv 3 18. −10x5 · 0.2x 3 19. wx17 · w17x 20. 7y 6z 3 · 3y 2z 3 21. −12c16d 9 · 0.5c0d 7 22. 0.875ef 0 · −16e 2f 23. (9g 2)(9h3) 24. (10i )2(0.01i 9) 25. 16j 10k6 · (0.5j 5k2)3 Algebra 395 Answer Page Back to Lesson 8-2 Name 8-2B page 2 PROPERTIES Objective G In 26–33, solve for x and y and name the power property used to find the solution. 26. 25 · 2 x = 215 27. 4x · 4x = 410 28. (63)x = 612 29. (7x)x = 7 9 30. (a3 · a x)2 = a6 31. c 4(c 3)x = c10 x 32. de 2 · 3d ey = 3d 3e5 x 33. ( fg) · f 3g 4 = f 9g 10 35. Write a multiplication problem that uses the Power of a Power Property to get an answer of m20. 396 Algebra Copyright © Wright Group/McGraw-Hill 34. Write a multiplication problem that uses the Product of Powers Property to get an answer of k17. Back to Lesson 8-3 Answer Page Name 8-3B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objective A In 1 and 2, a fraction is given. a. Write the numerator and denominator in expanded form. b. Simplify the fraction. 10j 5k3 2. _____ 2 a5 1. __ a2 12j k a. a. b. b. In 3–13, simplify. −c10 3. ___ c7 3.10 × 108 4. ________ 3 3.9 × 106 5. _______ 3 × 104 3d 3 6. ___ 6d 22e5 7. ____ 11e3 16f 6 8. ____6 2 × 10 −4f 10 27g 9. ____ 18g 4 −24h11 10. _____ 7 (−2)x 11. ____ (−2)y 30m8n4 12. ______ 5 2 42m n 4 81p r 13. ______ −36pr 4 398 Algebra Copyright © Wright Group/McGraw-Hill 9h Back to Lesson 8-3 Answer Page Name 8-3B page 2 PROPERTIES Objective G 14. Write an algebraic fraction for which you can use the Quotient of Powers Property to simplify to 3x 5. In 15–19, use the Quotient of Powers Property to find the value of x. x y 15. __ = y11 y3 513 4 16. ___ 5x = 5 18mx 6m4 17. ____3 = ____ 7 21m (−4)7 18. ____ = (−4)5 (−4)x (2y) 19. ____8 = (2y)12 x (2y) 9 m 20. Amber tried to simplify ___ , and she got m3. Explain the error she made m3 in simplifying the fraction. 21. Multiple Choice. Which expression can be simplified to 5m2x? 10mx A ____ 2mx 10m3x B _____ 2mx 10m6x C _____ 3x 10m8x D _____ 4x 2m 2m 5 22. Multiple Choice. Consider the equation __ = 56. Which statement 5n accurately describes the values of m and n? m Copyright © Wright Group/McGraw-Hill A m=n B m = 4 and n = 2 C m+n=6 D m-n=6 Algebra 399 Back to Lesson 8-4 Answer Page Name 8-4B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objectives A and B In 1 and 2, rewrite without negative exponents. 1. x −3 · y −4 2. 3a2b−5 In 3–8, rewrite: a. without fractions; b. without negative exponents. 32c−4 3. ____ 16c2 −d−2e2 4. _____ a. a. b. b. 5. ( __f1 ) −3 4 de (g ) 2 6. ___ −2 a. a. b. b. 70h4j−2k3 7. _______ 10h9k 4 −56m−6n−1 8. ________ 2 6 8m n a. a. b. b. In 9–14, give the answer as a simple fraction. 9. 4−3 11. ( __14 ) 10. 9−2 −1 Copyright © Wright Group/McGraw-Hill 13. (−2)−4 () 12. __56 −2 3 __ 14. (75)5 15. Order the following numbers from least to greatest. ( __34 )−2, __163 , (−3)(−4), ( __23 )−4 Algebra 401 Back to Lesson 8-4 Answer Page Name 8-4B page 2 PROPERTIES Objective G In 16–24, use the properties of negative exponents to find the value of x. p 1 __ 16. ___ px = 7 3 x 16 17. __4 = __ 9 r −2sx 1 18. ____ = ___ 3 2 6 t5 11 19. __ tx = t −3 () p s rs wx 8 21. ____ = __ 5 2−3w 4 1 20. 2−3 · w x = ___ 3 w 8w ( ) 2h−9 22. ____ 3hx 24. ( __21 ) -1 −3x 16 3h = ____ 2 −14 23. −14j−4k2x = ____ 4 10 jk =2 −2 x ? 26. Multiple Choice. Which expression can be simplified to __ 81 4 x −4 A __3 ) ( 402 Algebra ( ) x3 B __ 3 −1 ( )−4 3 C __x ( ) 3 D __ x3 −1 Copyright © Wright Group/McGraw-Hill 4 25. Justin simplified ( _25 ) , and he got __ . Explain the error he made in 25 simplifying the fraction. Back to Lesson 8-5 Answer Page Name 8-5B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objectives A, B and C In 1–3, simplify and give the answer as a simple fraction. () 1. 4 __21 4 ( 1 )4 2. 96 __4 In 3 and 4, an expression is given. a. Write the expression in expanded form. b. Simplify the expression. 3. (−7x)2 2a 3 4. __ 5b a. a. b. b. ( ) In 5–11, simplify and give the answer as a simple fraction. 5. (3y2)3 6. −(2m2)4 7. (−4n5)3 8. −(6pr2)2 9. 11. 2 ( ) · ( __43 )5 9 10. __4 ( __4c )2 49 3e ___ ( __ e )·( 7 ) 2 3 In 12–16, rewrite without parentheses and simplify. ( ) −3e5f 7 14. _____ 3 9 13. 4(−3c3d4)2 3 ( 2h ) −4 ___ h5 15. __ 2 7 · 5e f ( ) k 16. (6j 5k)2 · ___ 6 2j 404 Algebra 3 4 Copyright © Wright Group/McGraw-Hill 12. (2a2b)5 Back to Lesson 8-5 Answer Page Name 8-5B page 2 In 17–19, find the area of the figure. 17. 18. 17x2 cm 30 4x2y 3 ft 40 cm 19. 17x in. x3 in. 25x in. Area of a trapezoid is found by 1 __ 2 · height · (base 1 + base 2). PROPERTIES Objective G In 20–22, a. Tell what value of x will make the statement true for all values of the variables. Copyright © Wright Group/McGraw-Hill b. Identify the property that justifies the first step in simplifying the statement. 15 −32m 20. (−2m3n−1)x = ______ 5 n 6m x 72m2 21. 10 · ___3 = ____ 6 ( 5n ) a. a. b. b. 5n 22. x3 = −27m18n12 a. b. Algebra 405 Back to Lesson 8-6 Answer Page Name 8-6B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objectives D and E 1. The area of a square is 64 square units. What is the length of a side? In 2–10, write the exact value or approximate the number to the nearest hundredth. 2. √## 169 3. − √## 441 225 4. √## 5. √# 85 110 6. − √## 7. 81 2 1 __ 1 __ 1 __ 8. 34 2 9. −(196) 2 1 __ 10. −(13) 2 In 11–18, evaluate the expression. Write the exact value or approximate to the nearest hundredth. 1,048 - 24 11. √##### 1 __ 12. √### 9 + 64 1 __ 13. (16 + 81) 2 14. (25 + 144) 2 15. 3 √# 13 · √# 13 16. −2 √# 6 · √# 6 1 __ 2 ( ) · ( __107 ) 7 17. 4 __ 10 1 __ 2 19. Find the length of the missing side of the right triangle. 2 15 18. __3 · __ 8 1 __ 2 ( ) · ( __158 ) 1 __ 2 20. Veronica needs a new pole for her kite. What is the height, h, of the kite? Round to the nearest whole number. Copyright © Wright Group/McGraw-Hill 25 cm 15 x 15 cm 9 h 42.7 cm Algebra 407 Back to Lesson 8-6 Answer Page Name 8-6B page 2 21. If f (y) = 3 √#y √#y , what is f (8)? 22. Which of the expressions below are equal to (48)1/2? A 4 √# 3 B 2 √# 24 C 2 √# 12 D √# 6 · √# 8 In 23–32, write the exact value or approximate the number to the nearest hundredth. 3 9.261 23. √### 3 24. √## 125 3 25. √## −27 26. − √## 343 3 27. √## 512 28. 3 3 3 29. √## 1.2 · √## 1.2 · √## 1.2 3 3 3 30. √# 5 · √# 5 · √# 5 3 3 31. √# 64 · √# −8 3 3 3 32. √# 27 · √## −216 · √# −1 408 Algebra 3 √#__14 · √#__41 · √#__41 3 3 Copyright © Wright Group/McGraw-Hill 3 Back to Lesson 8-7 Answer Page Name 8-7B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objective D In 1–4, evaluate the expression. 1. √# 18 · √# 2 2. √##### 16 · 25 · 225 √# 99 3. ____ √# 73 4. ____ √# 11 √# 7 In 5–7, simplify. Give the exact value. Assume all variables are positive. 72 5. √# 6. 3 √## 160 7. 12 # √__ 9 In 8 and 9, write the exact value of the unknown in simplified form. 8. 9. 6 3 10 x y 10. A bowling ball manufacturer created a clear resin ball that can contain any colored figure. The maximum length of the figure can s __ where s represents the surface be found by the expression 2 √## 4π area of the ball. What is the length of the figure that can be placed in a ball with a surface area of 72.25π square inches? 11. Find the exact value of the area of a triangle with a base of 3 inches and a height of √# 6 inches. 4√# 410 Algebra Copyright © Wright Group/McGraw-Hill 5 Back to Lesson 8-7 Answer Page Name 8-7B page 2 In 12–23, simplify. Give the exact value. Assume all variables are positive. 12. √### 48a2b2 13. √### 56c2d5 250e 3f 6 14. − √### 15. −2√## 40 x 32y7 16. 5 √## 17. 3 √#### 112m4n8p5 ## 216h5 _____ 24h7 18. √ 20. ### 128s t √______ 50t 4 3 Copyright © Wright Group/McGraw-Hill 12n · √## 12n 22. 4 √## √### 147j 9k2 √### 12j 5k2 19. − _______ 10 ### √85xy 21. _______ 5 −2 5x y √### 23. √### 20d4e3 · √## 5d 2e Algebra 411 Back to Lesson 8-8 Answer Page Name 8-8B Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. REPRESENTATIONS Objectives I and J 1. A square has a diagonal with a length of 12 centimeters. a. Find the length of a side of the square. b. Find the area of the square. 2. The screen of a projection TV is 41.5 inches long and 28 inches tall. The length of the diagonal of the screen represents the size of the television. What is the size of the television? In 3 and 4, find the area of the figure. 3. 4. 24 25 20 12 In 5 and 6, find the exact length of a side of the cube. 5. A cube with volume 1,728 cubic inches 6. A cube with volume 648 cubic inches Copyright © Wright Group/McGraw-Hill 7. What is the volume of a cube with a side length of 8 inches? 8. What is the volume of a cube with a side whose diagonal 2 inches? measures 5 √# Algebra 413 Back to Lesson 8-8 Answer Page Name 8-8B page 2 In 9–13, find the distance between the given points. Give the exact simplified value. 9. (2, 6) and (7, 1) 10. (5, −7) and (8, 2) 11. (10, −12) and (9, −14) 12. (−7, −8) and (1, 2) 13. (−9, −9) and (−11, 5) y 14. Use the graph at the right to complete the following. 5 4 3 2 1 5 4 3 2 1 1 B (2, 1) x 1 2 3 4 5 C (5, 2) A (1, 2) 3 4 5 D (2, 5) a. What is the exact value of the distance between A and B? b. What is the exact value of the distance between C and D? c. What is the exact value of the perimeter of the rectangle? 15. Use the graph below to complete the following. 5 4 2 1 1 Y (3, 2) 3 4 5 x 1 3 4 5 Z (5, 2) a. What is the exact value of the distance between X and Z ? b. What is the exact value of the area of △XYZ ? 414 Algebra Copyright © Wright Group/McGraw-Hill y 5 4 X (3, 2) 3 2 1 Back to Lesson 8-9 Answer Page Name 8-9A Lesson Master Questions on SPUR Objectives See pages 521–523 for objectives. SKILLS Objective C In 1–6, rewrite without parentheses and without negative exponents. 5m2n 4 2. _____ 3 4 ( 4m n ) 6m n 4. (_______ 11m n ) 1. (2a 3b−4)3 −1 2 3. (−7x −4y 8) · (2x 5y)6 −2 4 −7 5. (6x 3y −6)−2 6. (−a 4b 2)−3 · (2a5b−6) PROPERTIES Objective F 7. Tell whether the pattern 3x 2 = x 3 is true for the given instances. b. x = 1 a. x = 0 c. x = 3 _1 8. Tell whether the pattern x 2 = √$x is true for the given instances. a. x = 0 b. x = 1 c. x = 4 9. Find a counterexample for the pattern x 2 · x 4 = x 8. 3a7b2 −2 10. Terri and Kandy both simplified ____ . State which property a5b−6 ( ) each student used for each step of their work. Terri’s Work Copyright © Wright Group/McGraw-Hill Step 1: (3a2b8)−2 a. Step 2: 3−2a−4b−16 b. 1 Step 3: _____ 4 16 c. 9a b Kandy’s Work (3a7b2)−2 (a b ) Step 1: _______ 5 −6 −2 −2 −14 −4 d. 3 a b Step 2: ________ −10 12 e. Step 3: 3−2a−4b−16 f. 1 Step 4: _____ 4 16 g. a b 9a b Algebra 415