Practice ? b a (-a) b a b (3a)

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1 Pratie 8- Zero and Negative Exponents Simplify eah expression ? ? ? (-6) (3.7) (-9) (-4.9) ? Evaluate eah expression for a 2 and b b a (-a) b a b (3a) (-b) a - b a -2 b a -2 b (3ab) -2 Simplify eah expression. 37. x xy a -5 b 40. m 2 n x 27 a 24 d 23 r 25 s x -6 y a -3 b s -9 t p -5 q -3 r m 28 n 52. d 24 e 27 3m 24 n 28 Write eah number as a power of 0 using a negative exponent ,000,000,000 0,000,000 Write eah expression as a deimal ? ? 0-4 Evaluate eah expression for m 4, n 5, and p 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 n -m n p p 2 n 2m a 22 b 2 d 23,000,000,000 2 Lesson 8- Pratie Algebra Chapter 8

2 Pratie 8-2 Sientifi Notation Write eah number in standard notation Write eah number in sientifi notation. 7. 5,000, ,000,000, billion million thousandths millionths thousand hundredths ,000,900,000,000 Order the numbers in eah list from least to greatest ,6 0-8,5 0-6, , , , ,040, , , ,5 0-3,8 0-2,4 0 - Simplify. Write eah answer using sientifi notation (3 0 5 ) 38. 5(7 0-2 ) 39. 8(9 0 9 ) 40. 7(9 0 6 ) 4. 3( ) 42. 2( ) 43. 3( ) 44. 3( ) 45. 3( ) Complete the table Units of Area in Square Feet Unit Standard Form Sientifi Notation in link rod mi m hetare Algebra Chapter 8 Lesson 8-2 Pratie 3

3 Pratie 8-3 Multipliation Properties of Exponents Simplify eah expression.. (3d -4 )(5d 8 ) 2. (-8m 4 )(4m 8 ) 3. n -6? n a 3? a ? (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 (8d 4 )(4d 7 ) 4. x -9? x 3? x ? r 7? s 4? s? r 3 7. b 7? b 3 8. (7p 4 )(5p 9 ) ? 2-9? (6r 4 s 3 )(9rs 2 ) ? m 2? m s 7? t 4? t (-3xy 6 )(3.2x 5 y) ? h 7? h 3 t 25? t ƒ 5? ƒ 2? ƒ r 6? r ? 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. ( )(2 0-5 ) 34. (4 0 9 )( ) 35. ( )(2 0-5 ) 36. (5 0 7 )(4 0 3 ) 37. (6 0-6 )( ) 38. (4 0 6 )(9 0 8 ) 39. ( )(8 0 4 ) 40. ( )(4 0-7 ) 4. ( )(3 0 ) 42. (9 0 2 )( ) 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 )( ) 48. (5 0 8 )( ) 49. In 990, the St. Louis metropolitan area had an average of g/m 3 of pollutants in the air. How many grams of pollutants were there in m 3 of air? 50. Light travels approximately mi in one year. This distane is alled a light-year. Suppose a star is light-years away. How many miles away is that star? 5. The weight of m 3 of air is approximately g. Suppose that the volume of air inside of a building is m 3. How muh does the air inside the building weigh? 52. Light travels in. in seond. How far will light travel in nanoseond or 0-9 s? 4 Lesson 8-3 Pratie Algebra Chapter 8

4 Pratie 8-4 More Multipliation Properties of Exponents Simplify eah expression.. (4a 5 ) 3 2. (2-3 ) 4 3. (m -3 n 4 ) (x 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 ) (a 3 b 4 ) -2 (a -3 b -5 ) (x 2 y) 4 6. (2b -2 ) 2 7. (m -5 ) (x -4 ) 5 (x 3 y 2 ) 5 9. (y 6 ) -3? y n 6? (n -2 ) 5 2. (m 5 ) -3 (m 4 n 5 ) (a 3 ) b -9? (b 2 ) (4 - s 3 ) (5a 3 b 5 ) (b -3 ) (y 6 ) a -4? (a 4 b 3 ) (x 4 y) d 3? (d 2 ) 5 Simplify. Write eah answer in sientifi notation ? (2 0 2 ) (3 0-6 ) ? (4 0 6 ) (9 0 7 ) ? (2 0 3 ) (7 0 5 ) (5 0 5 ) (2 0-3 ) (5 0 2 ) (3 0 5 ) 4 4. (4 0 8 ) ( 0-5 ) ? (8 0 7 ) (0 2 ) 3 (6 0-3 ) ? (2 0 2 ) 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 kg. The ar is traveling at 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 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 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 seonds? Algebra Chapter 8 Lesson 8-4 Pratie 5

5 Pratie 8-5 Division Properties of Exponents Simplify eah expression. x 7 y 9 z a x3 y z 25 b x 4 y 7 z a a a b a 6 b a 7 b 6 2. a 22 b a 5 b a 5a0 b 4 2 z a b z b 7. m 6 8. a 23 m 4 n 2 9. a s t2 b22 p 2 b 0 m 0 2. a x23 y h xz 24 b h x 5 y a m23 n x 2 y 9 n 22 b n a r3 s 2 3. n 28 r 2 s 6 b2 n n 5 b 2b4 Simplify eah quotient. Write eah answer in sientifi notation billion million billion million million billion trillion billion The half-life of uranium-238 is years. The half-life of uranium-234 is 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 million 985 million 6 Lesson 8-5 Pratie Algebra Chapter 8

6 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, , 7. 3, 3, 5 3, 2 3, 8. 20, 4, 4 5, 25 4, , -40, -6, -6.4, 0. 40, 20, 0, 5, Determine whether eah sequene is arithmeti or geometri.. -8, -0, -2.5, , 2. 5,, -3, -7, 3., 2 5, 25 4, 8 25, , -0.02, , , 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, , -0, 0, , 23., 4, 6, 64, 24. 6, 2, 24, 48, , 25, 5,, , 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

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 $ 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 y = 8? a 5 x 2 b Evaluate eah funtion rule for the given values. 22. y = 5.5 x for x =, 3, and y = 4?.5 x for x = 2, 4, and y = 3? 4 x for x =, 3, and y = 6 x for x = 2, 3, and y = 0.7 x for x =, 3, and y = 3. x for x =, 2, and y = 80? 0.5 x for x = 0, -2, and y = 4.3 x for x = -2, -, and y = 00? 0. x for x = -4, -, and 2 3. y = 5 x for x = -2, -3, and 4 Solve eah equation x = ? 4 x = x = 35. 4? 5 x = Lesson 8-7 Pratie Algebra Chapter 8

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 d 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 b., ,800 d. 34, 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 d 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