Pratie 8- Zero and Negative Exponents Simplify eah expression.. 6 0 2. 4-2 3. 3-3 4. 8-4 5. 6. 4 7. 3 8. 2 2 2 25 4 23 6 2 2 25 9. 3? 8 0 0. 6? 2-2. 2-2. -7-2 3. 6? 4 0 4. 9 0 5. 32 2 6. 9 8 2 2 2 7. 8 22 8. 9 2 9. 5(-6) 0 20. (3.7) 0 4 0 3 22 2. (-9) -2 22. (-4.9) 0 23. -6? 3-4 24. 7 22 4 2 Evaluate eah expression for a 2 and b 6. 25. b -2 26. a -3 27. (-a) -4 28. -b -3 29. 4a -3 30. 2b -2 3. (3a) -2 32. (-b) -2 33. 2a - b -2 34. -4a -2 b -3 35. 3-2 a -2 b - 36. (3ab) -2 Simplify eah expression. 37. x -8 38. xy -3 39. a -5 b 40. m 2 n -9 4. 42. 3 43. 5 44. 6 x 27 a 24 d 23 r 25 s 2 45. 3x -6 y -5 46. 8a -3 b 2-2 47. 5s -9 t - 48. -7p -5 q -3 r 2 49. 50. 5. 6m 28 n 52. d 24 e 27 3m 24 n 28 Write eah number as a power of 0 using a negative exponent. 53. 54. 55. 56. 0,000,000,000 0,000,000 Write eah expression as a deimal. 57. 0-5 58. 0-8 59. 4? 0-60. 6? 0-4 Evaluate eah expression for m 4, n 5, and p 2. 6. m p 62. n m 63. p p 64. n p 65. m p n 66. m -n 67. p -n 68. mn p 69. p -m 70. m 7. 72. -n -m n p p 2 n 2m a 22 b 2 d 23,000,000,000 2 Lesson 8- Pratie Algebra Chapter 8
Pratie 8-2 Sientifi Notation Write eah number in standard notation.. 7 0 4 2. 3 0-2 3. 2.6 0 5 4. 7. 0-4 5. 5.7 0-5 6. 4.55 0. 3.007 0 2 8. 9.407 0-5 9. 3.3 0 6 0. 83.7 0-4. 0.08 0-2. 0.06 0 5 3. 8.0023 0-3 4. 6.902 0 8 5. 005 0 2 6. 0.095 0 - Write eah number in sientifi notation. 7. 5,000,000 8. 975,000,000,000 9. 0.0000002 20. 0.000005008 2. 560 billion 22. 0.5 million 23. 2 thousandths 24. 095 millionths 25. 94 0 3 26. 54 0-3 27. 0.05 0 6 28. 0.03 0-4 29. 790 thousand 30. 25 hundredths 3. 0.00000000059 32. 5,000,900,000,000 Order the numbers in eah list from least to greatest. 33. 7 0-7,6 0-8,5 0-6,4 0-0 34. 5.0 0-4,4.8 0-3,5.2 0-2,5.6 0-2 35. 62,040, 6.2 0 2, 6.207 0 3,6.34 0-36. 0-3,5 0-3,8 0-2,4 0 - Simplify. Write eah answer using sientifi notation. 37. 4(3 0 5 ) 38. 5(7 0-2 ) 39. 8(9 0 9 ) 40. 7(9 0 6 ) 4. 3(.2 0-4 ) 42. 2(6. 0-8 ) 43. 3(.2 0-4 ) 44. 3(4.3 0-4 ) 45. 3(3.2 0-2 ) Complete the table. 46. 47. 48. 49. 50. 5. Units of Area in Square Feet Unit Standard Form Sientifi Notation in. 2 6.9444 0-3 link 2 0.4356 rod 2 272.25 mi 2 2.78 0 7 m 2 0.00076 hetare.08 0 7 Algebra Chapter 8 Lesson 8-2 Pratie 3
Pratie 8-3 Multipliation Properties of Exponents Simplify eah expression.. (3d -4 )(5d 8 ) 2. (-8m 4 )(4m 8 ) 3. n -6? n -9 4. a 3? a 5. 3 8? 3 5 6. (3p -5 )(6p ) 7. p 7? q 5? p 6 8. (-.5a 5 b 2 )(6a) 9. (-2d 3 e 3 )(6d 4 e 6 ) 0.. p 5? q 2? p 4 2. b 27? b 5 n 7? n 25 3. (8d 4 )(4d 7 ) 4. x -9? x 3? x 2 5. 2 3? 2 2 6. r 7? s 4? s? r 3 7. b 7? b 3 8. (7p 4 )(5p 9 ) 9. 2 8? 2-9? 2 3 20. (6r 4 s 3 )(9rs 2 ) 2. 4 3? 4 2 22. m 2? m -4 23. s 7? t 4? t 8 24. (-3xy 6 )(3.2x 5 y) 25. 5-7? 5 9 26. 27. h 7? h 3 t 25? t 23 28. ƒ 5? ƒ 2? ƒ 0 29. r 6? r -3 30. 5-6? 5 4 Simplify eah expression. Write eah answer in sientifi notation. 3. (7 0 7 )(5 0-5 ) 32. (3 0 8 )(3 0 4 ) 33. (9.5 0-4 )(2 0-5 ) 34. (4 0 9 )(4. 0 8 ) 35. (7.2 0-7 )(2 0-5 ) 36. (5 0 7 )(4 0 3 ) 37. (6 0-6 )(5.2 0 4 ) 38. (4 0 6 )(9 0 8 ) 39. (6. 0 9 )(8 0 4 ) 40. (2. 0-4 )(4 0-7 ) 4. (.6 0 5 )(3 0 ) 42. (9 0 2 )(0.3 0-8 ) 43. (4 0 9 )( 0 3 ) 44. (5 0 3 )(9 0-9 ) 45. (7 0 6 )(4 0 9 ) 46. (6 0-8 )(2 0-7 ) 47. (6 0 5 )(3.2 0 2 ) 48. (5 0 8 )(2.6 0-6 ) 49. In 990, the St. Louis metropolitan area had an average of 82 0-6 g/m 3 of pollutants in the air. How many grams of pollutants were there in 2 0 3 m 3 of air? 50. Light travels approximately 5.87 0 2 mi in one year. This distane is alled a light-year. Suppose a star is 2 0 4 light-years away. How many miles away is that star? 5. The weight of m 3 of air is approximately.3 0 3 g. Suppose that the volume of air inside of a building is 3 0 6 m 3. How muh does the air inside the building weigh? 52. Light travels.8 0 0 in. in seond. How far will light travel in nanoseond or 0-9 s? 4 Lesson 8-3 Pratie Algebra Chapter 8
Pratie 8-4 More Multipliation Properties of Exponents Simplify eah expression.. (4a 5 ) 3 2. (2-3 ) 4 3. (m -3 n 4 ) -4 4. (x 5 ) 2 5. 2 5? (2 4 ) 2 6. (4x 4 ) 3 (2xy 3 ) 2 7. x 4? (x 4 ) 3 8. (x 5 y 3 ) 3 (xy 5 ) 2 9. (5 2 ) 2 0. (a 4 ) -5? a 3. (3ƒ 4 g -3 ) 3 (ƒ 2 g -2 ) - 2. x 3? (x 3 ) 5 3. (d 2 ) -4 4. (a 3 b 4 ) -2 (a -3 b -5 ) -4 5. (x 2 y) 4 6. (2b -2 ) 2 7. (m -5 ) -3 8. (x -4 ) 5 (x 3 y 2 ) 5 9. (y 6 ) -3? y 2 20. n 6? (n -2 ) 5 2. (m 5 ) -3 (m 4 n 5 ) 4 22. (a 3 ) 6 23. b -9? (b 2 ) 4 24. (4 - s 3 ) -2 25. (5a 3 b 5 ) 4 26. (b -3 ) 6 27. (y 6 ) 3 28. a -4? (a 4 b 3 ) 2 29. (x 4 y) 3 30. d 3? (d 2 ) 5 Simplify. Write eah answer in sientifi notation. 3. 0-9? (2 0 2 ) 2 32. (3 0-6 ) 3 33. 0 4? (4 0 6 ) 3 34. (9 0 7 ) 2 35. 0-3? (2 0 3 ) 5 36. (7 0 5 ) 3 37. (5 0 5 ) 4 38. (2 0-3 ) 3 39. (5 0 2 ) -3 40. (3 0 5 ) 4 4. (4 0 8 ) -3 42. ( 0-5 ) -5 43. 0 5? (8 0 7 ) 3 44. (0 2 ) 3 (6 0-3 ) 3 45. 0 7? (2 0 2 ) 4 46. The kineti energy, in joules, of a moving objet is found by using the formula E = 2mv 2, where m is the mass and v is the speed of the objet. The mass of a ar is.59 0 3 kg. The ar is traveling at 2.7 0 m/s. What is the kineti energy of the ar? 47. The moon is shaped somewhat like a sphere. The surfae area of the moon is found by using the formula S = 2.56r 2. What is the surfae area of the moon if the radius is.08 0 3 mi? 48. Beause of a reord orn harvest, exess orn is stored on the ground in a pile. The pile is shaped like a one. The height of the pile is 25 ft, and the radius of the pile is.2 0 2 ft. Use the formula V 5 3 pr2 h to find the volume. 49. Suppose the distane in feet that an objet travels in t seonds is given by the formula d = 64t 2. How far would the objet travel after.5 0 3 seonds? Algebra Chapter 8 Lesson 8-4 Pratie 5
Pratie 8-5 Division Properties of Exponents Simplify eah expression. x 7 y 9 z 3. 2. a x3 y 22 24 5 3. 4. 9 z 25 b x 4 y 7 z 8 5. 6. 7. a 2 22 3 7 a a3 8. 3 b 3 4 9. a 6 b 25 0. 7 24. a 7 b 6 2. a 22 b 7 7 27 a 5 b 3. 4. 5. a 5a0 b 4 2 z a2 3 22 7 6. 2 3b z 23 23 b 7. m 6 8. a 23 m 4 n 2 9. a s24 20. t2 b22 p 2 b 0 m 0 2. a x23 y 22 22. h 23 23. 4 6 24. xz 24 b h 28 4 8 25. x 5 y 3 26. a m23 n 4 27. 4 2 x 2 y 9 n 22 b4 4 2 28. 29. n 9 30. a r3 s 2 3. n 28 r 2 s 6 b2 n 4 32. n 5 b 2b4 Simplify eah quotient. Write eah answer in sientifi notation. 33. 3.54 3 0 29 34. 9.35 3 0 23 35. 495 billion 36. 6.5 3 0 25 3.7 3 0 25 23.9 million 37. 9.5 3 0 9 38. 6.4 3 0 9 39. 298 billion 40. 5 3 0 2 8 3 0 7 49 million 4. 3.6 3 0 6 42. 8.9 3 0 7 43. 65 million 44. 9 3 0 23 4.76 3 0 22 9.5 billion 45. 36.2 trillion 46. 3.9 3 0 3 47. 5.6 3 0 25 48. 98.5 billion.3 3 0 8 8 3 0 27 49. The half-life of uranium-238 is 4.5 0 9 years. The half-life of uranium-234 is 2.5 0 5 years. How many times greater is the half-life of uranium-238 than that of uranium-234. a a2 b 3b5 a p23 q 22 q 23 r 5 b 4 a a2 b 24 b 2 b 5 x 4 y 28 z 22 x 2 y 6 z 20 a 2a3 b 22 3 b 5 a 3 b 3 a a8 b 6 a b5 m 8 n 3 m 0 n 5 8 3 0 9 4 3 0 5.8 3 0 28 0.9 3 0 3 4.9 3 0 2 7 3 0 3 40 million 985 million 6 Lesson 8-5 Pratie Algebra Chapter 8
Pratie 8-6 Geometri Sequenes Find the next three terms of eah sequene.. 4, 2, 36, 08, 2. 2, -8, 32, -28, 3. 8, 9, 9 2, 9 4, 4., 2 3, 9, 2 27, 5. -2, 20, -200, 2000, 6. 30, -0, 0, 2 0 3 9, 7. 3, 3, 5 3, 2 3, 8. 20, 4, 4 5, 25 4, 9. -00, -40, -6, -6.4, 0. 40, 20, 0, 5, Determine whether eah sequene is arithmeti or geometri.. -8, -0, -2.5, -5.625, 2. 5,, -3, -7, 3., 2 5, 25 4, 8 25, 4. -0.2, -0.02, -0.002, -0.0002, 5. -0, -5, 0, 5, 6. 6, -3, 3 2, 23 4, Write a rule for eah sequene. 7. 4, 2, 36, 08, 8. 2, -8, 32, -28, 9. 8, 9, 9 2, 9 4, 20., 2 3, 9, 2 27, 2. -2, 20, -200, 2000, 22. 30, -0, 0, 2 0 3 9, 23., 4, 6, 64, 24. 6, 2, 24, 48, 25. 25, 25, 5,, 26. 50, 25, 2.5, 6.25, Find the first, fourth, and eighth terms of eah sequene. 27. A(n) = 2? 3 n- 28. A(n) = 3? 4 n- 29. A(n) = 3? 2 n- 30. A(n) = -? 5 n- 3. A(n) = 4? 2 n- 32. A(n) = 2? 2 n- 33. A(n) = 0.? 4 n- 34. A(n) = -2.? 3 n- 35. A(n) = 0? 5 n- Write a rule and find the given term in eah geometri sequene desribed below. 36. What is the sixth term when the first term is 4 and the ommon ratio is 3? 37. What is the fifth term when the first term is -2 and the ommon ratio is 22? 38. What is the tenth term when the first term is 3 and the ommon ratio is -.2? 39. What is the fourth term when the first term is 5 and the ommon ratio is 6? 40. Suppose a manufaturer invented a omputer hip in 978 that had a omputational speed of s. The ompany improves its hips so that every 3 years, the hip doubles in speed. What would the hip s speed have been for the year 2002? Write your solution in terms of s. Algebra Chapter 8 Lesson 8-6 Pratie 7
Pratie 8-7 Exponential Funtions Complete the table for eah exerise.. Investment inreases by 2. The number of animals 3. The amount of matter.5 times every 5 yr. doubles every 3 mo. halves every year. Time Value of Number of Amount Time Time Investment Animals of Matter Initial $800 Initial 8 Initial 3200 g 5 yr $200 3 mo 36 yr 600 g 0 yr $800 6 mo 72 2 yr 800 g 5 yr $2700 9 mo 7 3 yr 7 20 yr 7 2 mo 7 25 yr 7 Evaluate eah funtion for the domain { 2, 0,, 2, 4}. 4. y = 2 x 5. y = 3. x 6. y = 0.8 x 7. y = 2? 4 x 8. y = 0? 3 x 9. y = 25? 5 x 0. y =. y = 00? a x a 2 x 2. y =? 8 3 b 0 b 4 x Graph eah funtion. 3. y = 3 x 4. y = 6 x 5. y =.5 x 6. y = 7 x 7. y = 0? 5 x 8. y = 6? 0.5 x 9. y =? 2 x 20. y =? 4 x 8 2 2. y = 8? a 5 x 2 b Evaluate eah funtion rule for the given values. 22. y = 5.5 x for x =, 3, and 4 23. y = 4?.5 x for x = 2, 4, and 5 24. y = 3? 4 x for x =, 3, and 5 25. y = 6 x for x = 2, 3, and 4 26. y = 0.7 x for x =, 3, and 4 27. y = 3. x for x =, 2, and 3 28. y = 80? 0.5 x for x = 0, -2, and 2 2 29. y = 4.3 x for x = -2, -, and 0 30. y = 00? 0. x for x = -4, -, and 2 3. y = 5 x for x = -2, -3, and 4 Solve eah equation. 32. 5 x = 625 33. 2? 4 x = 28 34. 4 x = 35. 4? 5 x = 64 25 4 8 Lesson 8-7 Pratie Algebra Chapter 8
Pratie 8-8 Exponential Growth and Deay Write an exponential funtion to model eah situation. Find eah amount after the speified time.. Suppose one of your anestors invested $500 in 800 in an aount paying 4% interest ompounded annually. Find the aount balane in eah of the following years. a. 850 b. 900. 2000 d. 200 2. Suppose you invest $500 in an aount paying 4.75% annual interest. Find the aount balane after 25 yr with the interest ompounded the following ways. a. annually b. semiannually. quarterly d. monthly 3. The starting salary for a new employee is $25,000. The salary for this employee inreases by 8% per year. What is the salary after eah of the following? a. yr b. 3 yr. 5 yr d. 5 yr 4. Carbon-4 has a half-life of 5,700 years. Sientists use this fat to determine the age of things made of organi material. Suppose the average page of a book ontaining approximately 0.5 mg of arbon-4 is put into a time apsule. How muh arbon-4 will eah page ontain after eah of the following numbers of years? a. 5700 b.,400. 22,800 d. 34,200 5. The tax revenue that a small ity reeives inreases by 3.5% per year. In 990, the ity reeived $250,000 in tax revenue. Determine the tax revenue in eah of the following years. a. 995 b. 998. 2000 d. 2006 6. Suppose the areage of forest is dereasing by 2% per year beause of development. If there are urrently 4,500,000 ares of forest, determine the amount of forest land after eah of the following. a. 3 yr b. 5 yr. 0 yr d. 20 yr 7. A $0,500 investment has a 5% loss eah year. Determine the value of the investment after eah of the following. a. yr b. 2 yr. 4 yr d. 0 yr 8. A ity of 2,950,000 people has a 2.5% annual derease in population. Determine the ity s population after eah of the following. a. yr b. 5 yr. 5 yr d. 25 yr 9. A $25,000 purhase dereases 2% in value per year. Determine the value of the purhase after eah of the following. a. yr b. 3 yr. 5 yr d. 7 yr Algebra Chapter 8 Lesson 8-8 Pratie 9