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Lesson 13.1 Skills Practice Name_________________________________________________________ Date__________________________ Exponentially Speaking Powers and Exponents Vocabulary Write the term that best completes each statement. 1. The exponent of a power is the number of times that the factor is repeatedly multiplied. 2. An expression used to represent a factor as repeated multiplication is called a power . 3. The base of a power is the repeated factor in a power. Problem Set State the base and the exponent of each power. 1. 94 The base is 9 and the exponent is 4. 3. 186 The base is 18 and the exponent is 6. 5. 2119 The base is 11 and the exponent is 9. 7. (215)2 © 2011 Carnegie Learning The base is 215 and the exponent is 2. 9. 73x3 The bases are 7 and x. The exponent is 3. 11. (222y)4 The base is 222y and the exponent is 4. 2. 102 The base is 10 and the exponent is 2. 4. 27 The base is 2 and the exponent is 7. 6. 2483 The base is 48 and the exponent is 3. 8.(214)6 The base is 214 and the exponent is 6. 10.(13x)2 The base is 13x and the exponent is 2. 12.2(71y)5 The base is 71y and the exponent is 5. Chapter 13 Skills Practice • 869 Lesson 13.1 Skills Practice page 2 Write each power in expanded notation and evaluate to calculate the product. 13. 4 3 14. 2 4 The expanded notation The expanded notation is (4)(4)(4) 5 64. is (2)(2)(2)(2) 5 16. 15. 5 4 16. 7 5 The expanded notation The expanded notation is (5)(5)(5)(5) 5 625. is (7)(7)(7)(7)(7) 5 16,807. 17. 3 8 18. 63 The expanded notation The expanded notation is (3)(3)(3)(3)(3)(3)(3)(3) 5 6561. is (6)(6)(6) 5 216. Write each power in expanded notation and evaluate to calculate the product. 20. (24)5 The expanded notation is The expanded notation is (28)(28)(28) 5 2512. (24)(24)(24)(24)(24) 5 21024. 21. (23)4 22. (26)6 The expanded notation is The expanded notation is (23)(23)(23)(23) 5 81. (26)(26)(26)(26)(26)(26) 5 46,656. 23. 2(25) 24. 2(56) The expanded notation is The expanded notation is 2(2)(2)(2)(2)(2) 5 232. 2(5)(5)(5)(5)(5)(5) 5 215,625. 25. 2(72) 26. 2(83) The expanded notation is The expanded notation is 2(7)(7) 5 249. 2(8)(8)(8) 5 2512. 870 • Chapter 13 Skills Practice © 2011 Carnegie Learning 19. (28)3 Lesson 13.1 Skills Practice page 3 Name_________________________________________________________ Date__________________________ Write each expression in expanded notation and evaluate to calculate the product. 27. (4)2(25)3 28. (24)4(7)2 The expanded notation is The expanded notation is (4)(4)(25)(25)(25) 5 22000. (24)(24)(24)(24)(7)(7) 5 12,544. 29. (2)5(26)2 30. (22)5(8)3 The expanded notation is The expanded notation is (2)(2)(2)(2)(2)(26)(26) 5 1152. (22)(22)(22)(22)(22)(8)(8)(8) 5 216,384. 31. 2(3)6(2)4 32. 2(6)3(4)2 The expanded notation is The expanded notation is 2(3)(3)(3)(3)(3)(3)(2)(2)(2)(2) 5 211,664. 2(6)(6)(6)(4)(4) 5 23456. 33. 2(4)3(8)2 34. 2(5)3(9)2 The expanded notation is The expanded notation is 2(4)(4)(4)(8)(8) 5 24096. 2(5)(5)(5)(9)(9) 5 210,125. Write each expression in expanded notation. © 2011 Carnegie Learning 35. 3 2 x3 36. 2 5y2 The expanded notation is The expanded notation is (3)(3)(x)(x)(x). (2)(2)(2)(2)(2)( y)( y). 37. 5 2 y4 38. x 5 z2 The expanded notation is The expanded notation is (5)(5)( y)( y)( y)( y). (x)(x)(x)(x)(x)(z)(z). Chapter 13 Skills Practice • 871 Lesson 13.1 Skills Practice 39. (5x)4 The expanded notation is page 4 40. (7x)2 The expanded notation is (7x)(7x). (5x)(5x)(5x)(5x). 41. (6z)3 42. (2xy)5 The expanded notation is The expanded notation is (6z)(6z)(6z). (2xy)(2xy)(2xy)(2xy)(2xy). 43. 5x3 The expanded notation is 5(x)(x)(x). 44. 4y5 The expanded notation is 4( y)( y)( y)( y)( y). Write each expression in expanded notation. 46. 2(6y)3 The expanded notation is The expanded notation is 2(7z)(7z)(7z)(7z)(7z). 2(6y)(6y)(6y). 47. (24a)3 48. (22b)6 The expanded notation is The expanded notation is (24a)(24a)(24a). (22b)(22b)(22b)(22b)(22b)(22b). 49. 28z4 50. 26m7 The expanded notation is The expanded notation is 28(z)(z)(z)(z). 26(m)(m)(m)(m)(m)(m)(m). 51. 2(3x)2 y4 52. (28y)3 z2 The expanded notation is The expanded notation is 2(3x)(3x)( y)( y)( y)( y). (28y)(28y)(28y)(z)(z). 872 • Chapter 13 Skills Practice © 2011 Carnegie Learning 45. 2(7z)5 Lesson 13.1 Skills Practice page 5 Name_________________________________________________________ Date__________________________ Write each expression using exponents. 53. (7)(7)(7)(7) 54. 2 2 2 2 2 2 2 2 The power is 7 . The power is 28. 4 55. 4 4 4 4 4 4 56. (5)(5)(5)(5) The power is 4 . The power is 54 . 6 57. (23)(23)(23)(23)(23) The power is (23) . 5 59. 24 24 24 24 24 The power is (24)5. 61. 22 2 2 2 2 2 2 2 The power is 228. 58. 29 29 29 29 29 29 29 The power is (29)7. 60. 2(6)(6)(6)(6) The power is 264. 62. 25 5 5 The power is 253. Write each expression using exponents. 63. y y y y y 64. x x x x x x x x x The power is y . The power is x9. 5 65. (a)(a)(a)(a)(a)(a)(a) 66. b b b b b b The power is a . The power is b6 . © 2011 Carnegie Learning 7 67. 2z 2z 2z 2z 68. (2m)(2m)(2m)(2m)(2m)(2m) The power is (2z) . 4 69. 2b 2b 2b 2b 2b The power is (2b)5. 71. 2(x)(x)(x)(x) The power is 2x4. The power is (2m)6. 70. 2n n n n n The power is 2n5. 72. 2y y y y y y y y The power is 2y8. Chapter 13 Skills Practice • 873 Lesson 13.1 Skills Practice page 6 Write each expression using exponents. 74. (2a)(2a)(2a)(2a)(c)(c)(c)(c)(c) 73. (2x)(2x)(2x)(2y)(2y) The power is (2x)3(2y)2. 75. (2y) (2y) z z z z z The power is (2y)2z5. The power is (2a)4c5. 76. (2m) (2m) (2m) (2m) (2m) n n n The power is (2m)5n3. 78. 26 6 6 b b h h h 77. (2a)(2a)(2a)(b)(b)(b) The power is (2a)3b3. 79. 24 4 4 4 4 m m m n n The power is 263b2 h3. 80. 23 3 3 3 3 y y y y z z z The power is 245m3 n2. The power is 235y4z3. 81. 25 5 a a a a a b b 82 . 22 2 2 2 x x x y y y y The power is 25 a b . The power is 224x3y4. 2 5 2 Write each expression using exponents. The power is (3x)3y3z5 . 85. 5mn 5mn 5mn 5mn l l l The power is (5mn)4l3 . 84. 4a 4a 2b 2b 2b c c c c The power is (4a)2(2b)3c4. 86. (22x)(22x)(22x)( y)( y)(z)(z)(z) The power is (22x)3y2z3. 87. a a a (24b) (24b) c c 88. 26m 6m 6m 6m n n n The power is a (24b) c . The power is 2(6m)4n3. 3 2 2 89. 23x 3x 3x (22y) (22y) z z z z The power is 2(3x)3(22y)2z4. 874 • Chapter 13 Skills Practice © 2011 Carnegie Learning 83. 3x 3x 3x y y y z z z z z Lesson 13.2 Skills Practice Name_________________________________________________________ Date__________________________ Digital Storage Multiplying and Dividing Powers Problem Set Write each expression in expanded form. 1. 5 2 54 2. 3 4 35 555555 3. 7 3 75 333333333 4. 2 2 23 77777777 22222 Simplify each expression. Show your work. 5. (9)2(9)4 6. (24)3(24)7 (9)2(9)4 5 92 14 (24)3(24)7 5 (24)317 5 96 © 2011 Carnegie Learning 7. (22)2(22)5 5 (24)10 8. (28)4(28)5 (22)2(22)5 5 (22)215 (28)4(28)5 5 (28)415 5 (22)7 5 (28)9 Write each expression in expanded form. 9. x 2 x3 xxxxx 11. m5 m2 mmmmmmm 10. y y2 yyy 12. n 4 n5 nnnnnnnnn Chapter 13 Skills Practice • 875 Lesson 13.2 Skills Practice page 2 Simplify each expression. Show your work. 13. (2a)3(2a)4 14. (2b)2(2b)4 (2a)3(2a)4 5 (2a)314 (2b)2(2b)4 5 (2b)214 5 (2b)6 5 (2a)7 16. (2z)6(2z)2 15. (2c)(2c)3 (2c)(2c)3 5 (2c)113 (2z)6(2z)2 5 (2z)612 5 (2z)8 5 (2c)4 Simplify each expression. Show your work. 17. x 2y2x3y5 x2y2x3y5 5 (x2x3)( y2y5) a3 b2ab4 5 (a3a)(b2b4) 5 x2 13 y2 15 5 a311 b214 5 x5 y7 5 a4 b6 19. 7y3z4 2yz3 20. 3mn3 8m6n7 7y3z4 2yz3 5 (7 2)( y3y)(z4z3) 3mn3 8m6n7 5 (3 8)(m m6 )(n3n7) 5 14y311 z413 5 24m116 n3 17 5 14y4z7 5 24m7n10 876 • Chapter 13 Skills Practice © 2011 Carnegie Learning 18. a 3 b2ab4 Lesson 13.2 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 21. 5y3 3yz3 z2 22. 9b2 2a5 a2b6 5y3 3yz3 z2 5 (5 3)( y3y)(z3z2) 9b2 2a5 a2 b6 5 (9 2)(a5a2)(b2b6) 5 15y311 z3 12 5 18a512 b216 5 15y4z5 5 18a7b8 23. (2y)2 (2y)4 z z 24. (2m)2 n3 (2m)4 n2 (2y)2 (2y)4 z z 5 (2y)214 z111 (2m)2 n3 (2m)4 n2 5 [ (2m)2 (2m)4 ](n3 n2 ) 5 (2m)214 n312 5 (2m)6n5 5 (2y)6z2 25. 3x3 2x2 y3 y 26. (2b) 4a (2b)5 2a3 (2b) 4a (2b)5 2a35 (4 2) (a a3)[(2b)(2b)5] 5 6x312 y3 11 5 8a113 (2b)115 5 6x5y4 5 8a4(2b)6 © 2011 Carnegie Learning 3x3 2x2 y3 y 5 (3 2)(x3x2)( y3y) Chapter 13 Skills Practice • 877 Lesson 13.2 Skills Practice page 4 Simplify each expression. Show your work. 28. (43)5 27. (22)3 (22)3 5 22?3 (43)5 5 43?5 5 26 5 415 29. (72)4 30. (33)2 (72)4 5 72 ?4 (33)2 5 33?2 5 78 5 36 31. 2(22)4 32. 2(65)2 ) 2(22)4 5 2(22?4 2(65)2 5 2(65?2) 5 228 5 2610 Simplify each expression. Show your work. 34. ( y3)2 (x5)2 5 x5?2 5 x10 35. (m3)5 ( y3)2 5 y3?2 5 y6 36. (n4)3 (m3)5 5 m3?5 (n4)3 5 n4?3 5 m15 5 n12 37. (2b2)6 38. 2(m2)4 ) (2b2)6 5 (21)6(b2?6 5 b12 878 • Chapter 13 Skills Practice ) 2(m2)4 5 2(m2?4 5 2m8 © 2011 Carnegie Learning 33. (x5)2 Lesson 13.2 Skills Practice page 5 Name_________________________________________________________ Date__________________________ Simplify each expression. Show your work. 39. (3x2y)4 40. (2a2b3)5 (3x2y)4 5 34 (x2)4 y4 (2a2b3)5 5 25 (a2)5 (b3)5 5 81(x)24y4 5 25 (a)25(b)35 5 81x8y4 5 32a10b15 41. (24mn3)3 42. (25y3z2)5 (24mn3)3 5 (24)3m3(n3)3 (25y3z2)5 5 (25)5( y3)5 (z2)5 5 264m3(n)33 5 23125( y)35(z)25 5 264m3n9 523125 y15z10 43. (22cd2)4 44. (22x3y4 )2 (22x3y4)2 5 (22)2(x3)2( y4)2 5 16c4(d)24 5 4(x)3?2( y)4?2 5 16c4d8 5 4x6y8 © 2011 Carnegie Learning (22cd2)4 5 (22)4c4(d2)4 Chapter 13 Skills Practice • 879 Lesson 13.2 Skills Practice page 6 Write each numerator and denominator in expanded form. 4 45. __ 72 7 8 46. __ 45 4 ? 7 __________ 7 ? 7 ? 7 7?7 96 47. __ 2 9 ? 4 ? 4 ? 4?4 ______________________ 4 ? 4 ? 4 ? 4 4?4?4?4?4 9 48. __ 53 5 ? 9 ? 9 ________________ 9 ? 9 ? 9 ? 9 9?9 5 ? 5 ? 5 ? 5?5 _________________________ 5 ? 5 ? 5 ? 5 ? 5?5?5 Simplify each expression. Show your work. 68 50. __ 65 5 49. __ 32 3 __ 3522 32 5 __ 6 5 6825 5 33 5 63 8 5 65 3 9 52. ____ 3 2 23 ( 12 ) ( 3 ) 12 ___ _____ 212 5 2 4 4 3 __ ____ 3 2 5 2 2 5 2(12824) 5 2(3922 ) 52124 5 237 8 12 8 9 23 9 Write each numerator and denominator in expanded form. 5 y4 53. __ x3 54. __ 3 x y x ? x ? x ? x _____________ ? x x?x?x z7 55. __ 2 z z ? z ? z ? z ? z ? z ? z __________________ z?z 880 • Chapter 13 Skills Practice y?y?y?y __________ y?y?y 6 56. __ a3 a a ? a ? a ? a ? a?a ________________ a ? a ? a © 2011 Carnegie Learning 2128 51. _____ 4 12 Lesson 13.2 Skills Practice page 7 Name_________________________________________________________ Date__________________________ Simplify each expression. Show your work. m9 58. ___ 6 m n5 57. __ 4 n 5 __ n 5 n524 9 m926 ___ m6 5 n m 5 n 5 m3 4 b6 59. ____ 4 2b 2h14 60. _____ 6 h ( ) 6 6 ____ 2__ b b 5 b4 2 b4 14 6 h 6 5 2b624 5 2(h1426 ) 5 2b2 5 2h8 212x7 61. ______ 2 3x ( 3 )(x ) 24y8 62. ____ 4 4y ( 4 )(y ) 7 7 _____ ______ 212 __ x 212x 5 y 24y ___ _____ 24 __ 4 4 5 5 24(x722 ) 5 6( y824) 5 24x5 5 6y4 3x2 © 2011 Carnegie Learning ( h ) 14 _____ _____ 2h 5 2h 45a7b3 63. ______ 4 25a b 2 )(a )( b ) (25 7 3 7 3 _______ 45 __ a4 __ b 5 ___ 45a4b 25a b 8 8 4y 10m8n3 64. _______ 2m7 ( 2 )( m ) 8 _______ 10m n 5 ___ 10 ___ m (n3) 8 3 2m7 7 5 29(a724)(b321 ) 5 5(m827)(n3) 5 29a3b2 5 5mn3 Chapter 13 Skills Practice • 881 Lesson 13.2 Skills Practice page 8 Simplify each expression. Show your work. 65. 3a2 4a3 66. 25m8 7m2 3a2 4a3 5 (3 4)(a2 a3 ) 25m8 7m2 5 (25 7)(m8 m2 ) 5 (12)(a213 ) 5 (235)(m812 ) 5 12a5 5 235m10 67. (22b)3 3b4 68. (2n2)4 (22b)3 3b4 5 (22)3(b3) 3b4 (2n2)4 5 (24)(n2 4) 5 (22)3(3)(b3 b4 ) 5 16n8 5 (28)(3)(b314 ) 5224b7 69. (25mn3)2 70. (4y3)2 (23y)2 (25mn3)2 5 (25)2(m2)(n3 2) (4y3)2 (23y)2 5 (42)( y3 2)(23)2( y2) 5 25m2n6 5 (16)( y6)(9)( y2) 5 144y8 12g5 71. _____ 3 2g 5 72. _____ 14h4 2h ( 2 ) ( 2 ) 12g ___ _____ 3 5 12 g523 5 ___ _____ 14h 5 14 h524 5 6g2 5 7h 5 2g 882 • Chapter 13 Skills Practice 2h4 © 2011 Carnegie Learning 5 144( y612 ) Lesson 13.2 Skills Practice page 9 Name_________________________________________________________ Date__________________________ 232x8y5 ________ 73. 4x6y 40a5b7 74. _______ 28a2b6 ( 4 )( x )( y ) ( 8 )( a )( b ) 8 y 232x y _____ ________ 5 232 __ x __ ________ 40a2 b6 5 _____ 240 __ a2 __ b6 5 (28)(x82 6 )( y521 ) 5 (25)(a52 2 )(b726 ) 5 28x2y4 5 25a3b 8 5 5 5 4x6 y 28a b 6 ( 26 )( )( n ) 4 m ? m _____________ n 5 _____ 218 _______ __ n 218m ? m 2 4 26m n 3 5 7 56xy3 (x3y)2 y 76. ______________ 8x6 y 218m5 m2 n4 _____________ 75. 26m3 n 5 7 5 m3 2 56xy3 ? (x3)2y2 ? y 56xy3 ? (x3y)2y _______________ 5 _____________ 6 8x y 8x6 y ( )( )( ) 5 (3)(m51223)(n421 ) 3?2 y3 ? y2 ? y 5 ___ 56 ______ x ? x6 ________ y 8 x 5 3m4n3 5 (7)(x116–6 )( y3121121) © 2011 Carnegie Learning 5 7xy5 Chapter 13 Skills Practice • 883 © 2011 Carnegie Learning 884 • Chapter 13 Skills Practice Lesson 13.3 Skills Practice Name_________________________________________________________ Date__________________________ Extending the Rules Zero and Negative Exponents Problem Set Simplify each expression using the properties of powers. Express your solution in expanded notation, and then calculate the value. 3 1. __ 53 5 __ 53 5 5323 4 __ 2424 2 5 5 50 5 20 5 1 5 1 3 5 3. __ 7 72 2 24 6 4. __ 36 3 2 __ 7 5 7222 __ 36 26 3 5 5 70 5 30 5 1 5 1 7 2 © 2011 Carnegie Learning 4 2. __ 24 2 5. __ 4 49 9 6 36 6. __ 6 62 2 9 __ 4929 49 5 __ 6 5 6222 5 40 5 60 5 1 5 1 4 2 62 Chapter 13 Skills Practice • 885 Lesson 13.3 Skills Practice page 2 Simplify each expression using the Quotient Rule of Powers. 7. __ 2 24 0 8. __ 9 95 0 __ 2024 24 5 2 9 5 224 5 925 0 9. __ 8 83 0 0 __ 95 5 9025 10. __ 4 43 0 0 __ 43 5 4023 0 __ 83 5 8023 8 4 5 823 5 423 50 11. __ 8 5 12. __ 3 32 0 0 __ 32 5 3022 0 __ 58 5 5028 5 3 5 528 5 322 Rewrite each expression so that the exponent is positive. __ 1 32 15. 6 23 __ 1 63 17. 4 28 __ 1 48 886 • Chapter 13 Skills Practice 14. 5 29 __ 1 59 16. 2 25 __ 1 25 18. 7 23 __ 1 73 © 2011 Carnegie Learning 13. 3 22 Lesson 13.3 Skills Practice page 3 Name_________________________________________________________ Date__________________________ Rewrite each expression so that the exponent is positive. 19. x 23 20. y28 __ 1 x 3 __ 1 y8 21. a 28 b22 22. m24 n25 ____ 1 a8b2 23. y 24 z23 _____ 1 m4n5 24. x 22 y26 ____ 1 y4z3 ____ 1 x2y6 Rewrite each expression so that the exponent is positive. 25. ___ 1 225 26. ___ 1 623 5 2 27. ___ 1 924 3 6 28. ___ 1 422 2 4 4 9 29. ___ 1 723 30. ___ 1 524 4 5 73 © 2011 Carnegie Learning Rewrite each expression so that the exponent is positive. 31. ___ 1 y24 y 4 32. ___ 1 x27 x 7 33. ______ 1 x26y22 34. ______ 1 a23b28 x 6 y2 3 b8 a 35. _______ 1 m25 n29 36. _______ 1 g27 h24 m5n9 g7 h4 Chapter 13 Skills Practice • 887 Lesson 13.3 Skills Practice page 4 Simplify each expression. Show your work. y22 38. ___ 22 y 4 37. __ x4 x 4 __ x424 x4 5 x y22 y22 2 (22) 5 ___ y22 5 x0 5 y0 5 1 5 1 40. (20)(25) 39. (60)(63) (60)(63) 5 (1)(63) (20)(25) 5 (1)(25) 5 63 5 25 5 216 5 32 12x2y3 41. ______ 2 4x y 15a5b4 42. ______ 3a2b4 ( 4 ) ( 3 ) 12x y ______ 5 2 ___ 12 x222y321 ______ 15a2 b4 5 ___ 15 a522 b424 5 3x0y2 5 5a3b0 5 3y2 5 5a3 2 3 3a b 4 © 2011 Carnegie Learning 4x y 5 888 • Chapter 13 Skills Practice Lesson 13.3 Skills Practice page 5 Name_________________________________________________________ Date__________________________ Simplify each expression. Then, calculate the value. Do not leave your answer as a power. 2 43. __ 34 3 __ 3224 34 5 5 __ 4528 48 5 5 322 5 423 1 5 __ 32 1 5 __ 43 1 5 __ 9 1 5 ___ 64 2 3 45. (65)(627) © 2011 Carnegie Learning 5 44. __ 48 4 4 46. (24)(228) (65)(627) 5 651(27) (24)(228) 5 241(28) 5 622 5 224 1 5 __ 62 1 5 __ 24 1 5 ___ 36 1 5 ___ 16 523 47. ___ 526 25 48. ___ 322 3 523 5 5232(26) ___ 526 325 5 3252(22) ___ 322 5 53 5 323 5 125 1 5 __ 33 1 5 ___ 27 Chapter 13 Skills Practice • 889 Lesson 13.3 Skills Practice page 6 Simplify each expression so that the exponent is positive. Show your work. y3 49. __ 5 y 50. __ x x9 4 y __ 5 y325 y x 5 y22 5 x25 1 5 __ y2 5 __ 1 x5 3 5 a25 51. ___ a2 4 __ x9 5 x429 8 52. ___ c24 c a25 5 1 ____ ___ a2 a2a5 c8 5 c82(24) ___ c24 1 5 ____ a215 5 c12 1 5 __7 a x4y23 53. _____ 2 xy 3 2 54. _____ m5n6 mn xy _____ 5 x421 y2322 3 2 _____ m5n6 5 m325 n226 5 x3y25 5 m22 n24 x3 5 __ y5 1 5 _____ m2n4 4 23 xy mn © 2011 Carnegie Learning 2 890 • Chapter 13 Skills Practice Lesson 13.3 Skills Practice page 7 Name_________________________________________________________ Date__________________________ (x2y25) ? (xy) 55. ___________ x4y3 18a2b2 56. __________ 6ab3 ? ab24 x211 y2511 (x2y25) ? (xy) _________ 5 ___________ x4y3 x4y3 18a2b2 18a2b2 _________ 5 __________ 3 24 6ab ? ab 6a111 b324 x3y24 5 _____ x4y3 3a2b2 5 _____ a2b21 5 x324y2423 5 3a222b22(21) 5 x21 y27 5 3a0b3 1 5 ___ xy7 5 3b3 4 6 n 57. __________ 36m 2 3 4m n mn8 n 36m n ___________ 5 _________ 36m 2 3 8 211 318 5c215d311 5c2d3 ? c5d 5 _________ __________ 4 7 40c ? cd 40c411d7 9m4n6 5 ______ m3n11 cd 5 _____ 8c5d7 5 9m423n6211 1 c725d427 5 __ 8 5 9m1 n25 1 c 5 __ 2d23 8 9m 5 ____ n5 c 5 ____ 8d3 4 6 4m n ? mn © 2011 Carnegie Learning 2 3 5 58. __________ 5c d4 ? c d 40c ? cd7 4 6 4m n 7 4 2 Chapter 13 Skills Practice • 891 © 2011 Carnegie Learning 892 • Chapter 13 Skills Practice Lesson 13.4 Skills Practice Name_________________________________________________________ Date__________________________ Let’s Get Scientific! Scientific Notation Vocabulary Match each definition to its corresponding term. 1. a way to express a very large or very a. scientific notation small number as the product of a number between 1 and 10 and a power of 10 a. scientific notation 2. the decimal part of a number written in scientific notation; the number a in a 3 10 b. order of magnitude n c. mantissa 3. an estimate of size expressed as a c. mantissa power of 10 b. order of magnitude 4. the exponent of 10 for a number written d. characteristic in scientific notation; the number © 2011 Carnegie Learning n in a 3 10n d. characteristic Chapter 13 Skills Practice • 893 Lesson 13.4 Skills Practice page 2 Problem Set Write each number in scientific notation. Show your work. 2. 3700 1. 45,000,000 45,000,000 5 (4.5)(10,000,000) 3700 5 (3.7)(1000) 5 (4.5)(107) 5 (3.7)(103) The number written in scientific notation is The number written in scientific notation is 4.5 3 10 . 3.7 3 103. 7 4. 92,400,000,000 3. 562,000 562,000 5 (5.62)(100,000) 92,400,000,000 5 (9.24)(10,000,000,000) 5 (5.62)(105) 5 (9.24)(1010) The number written in scientific notation The number written in scientific notation is 5.62 3 10 . is 9.24 3 1010. 5 5. There are over 29,000 grains of long-grain rice in a one-pound bag. 29,000 5 (2.9)(10,000) 5 (2.9)(104) © 2011 Carnegie Learning The number written in scientific notation is 2.9 3 104. 894 • Chapter 13 Skills Practice Lesson 13.4 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 6. There are about 100,000,000,000 stars in our galaxy. 100,000,000,000 5 (1) (100,000,000,000) 5 (1)(1011) The number written in scientific notation is 1 3 1011. 7. The distance from the Earth to the Moon is about 385,000,000 meters. 385,000,000 5 (3.85)(100,000,000) 5 (3.85)(108) The number written in scientific notation is 3.85 3 108. 8. The average distance between the Earth and the Sun is about 93,000,000 miles. 93,000,000 5 (9.3)(10,000,000) 5 (9.3)(107) © 2011 Carnegie Learning The number written in scientific notation is 9.3 3 107. Write each number in standard notation. Show your work. 9. 5.2 3 107 5.2 3 107 5 (5.2)(107) 5 (5.2)(10,000,000) The number written in standard notation is 52,000,000. Chapter 13 Skills Practice • 895 Lesson 13.4 Skills Practice page 4 10. 3.7 3 108 3.7 3 108 5 (3.7)(108) 5 (3.7)(100,000,000) The number written in standard notation is 370,000,000. 11. 2.871 3 1011 2.871 3 1011 5 (2.871)(1011) 5 (2.871)(100,000,000,000) The number written in standard notation is 287,100,000,000. 12. 4.26 3 109 4.26 3 109 5 (4.26)(109) 5 (4.26)(1,000,000,000) 13. There are about 1 3 105strands of hair on the human head. 1 3 105 5 (1)(105) 5 (1)(100,000) The number written in standard notation is 100,000. 896 • Chapter 13 Skills Practice © 2011 Carnegie Learning The number written in standard notation is 4,260,000,000. Lesson 13.4 Skills Practice page 5 Name_________________________________________________________ Date__________________________ 14. The population of Texas is about 2.4 3 107 people. 2.4 3 107 5 (2.4)(107) 5 (2.4)(10,000,000) The number written in standard notation is 24,000,000. 15. The population of California is about 3.7 3 107people. 3.7 3 107 5 (3.7)(107) 5 (3.7)(10,000,000) The number written in standard notation is 37,000,000. 16. The circumference of the Earth at the equator is about 4.008 3 107meters. 4.008 3 107 5 (4.008)(107) 5 (4.008)(10,000,000) © 2011 Carnegie Learning The number written in standard notation is 40,080,000. Chapter 13 Skills Practice • 897 Lesson 13.4 Skills Practice page 6 Write each number in scientific notation. Show your work. 18. 0.000831 17. 0.000067 0.000067 5 (6.7)(0.00001) 0.000831 5 (8.31)(0.0001) 1 0.00001 5 ________ 100,000 1 0.0001 5 _______ 10,000 1 5 ___ 105 1 5 ___ 104 5 1025 5 1024 The number written in scientific notation is The number written in scientific notation is 6.7 3 10 . 8.31 3 1024. 25 20. 0.00000092 0.00000000253 5 (2.53)(0.000000001) 0.00000092 5 (9.2)(0.0000001) 1 0.000000001 5 _____________ 1,000,000,000 1 0.0000001 5 ___________ 10,000,000 5 ___ 1 109 5 ___ 1 107 5 1029 5 1027 The number written in scientific notation is The number written in scientific notation is 2.53 3 10 . 9.2 3 1027. 29 898 • Chapter 13 Skills Practice © 2011 Carnegie Learning 19. 0.00000000253 Lesson 13.4 Skills Practice page 7 Name_________________________________________________________ Date__________________________ 21. A grain of rice weighs about 0.025 grams. 0.025 5 (2.5)(0.01) 1 0.01 5 ____ 100 1 5 ___ 102 5 1022 The number written in scientific notation is 2.5 3 1022. 22. The diameter of a red blood cell is about 0.00004 inches. 0.00004 5 (4)(0.00001) 1 0.00001 5 ________ 100,000 1 5 ___ 105 5 1025 © 2011 Carnegie Learning The number written in scientific notation is 4 3 1025. Chapter 13 Skills Practice • 899 Lesson 13.4 Skills Practice page 8 23. A grain of salt weighs about 0.0000585 grams. 0.0000585 5 (5.85)(0.00001) 0.00001 5 ________ 1 100,000 5 ___ 1 105 5 1025 The number written in scientific notation is 5.85 3 1025. 24. A credit card is about 0.0299 inches thick. 0.0299 5 (2.99)(0.01) 1 0.01 5 ____ 100 1 5 ___ 102 5 1022 © 2011 Carnegie Learning The number written in scientific notation is 2.99 3 1022. 900 • Chapter 13 Skills Practice Lesson 13.4 Skills Practice page 9 Name_________________________________________________________ Date__________________________ Write each number in standard notation. Show your work. 25. 8.3 3 1025 26. 6.22 3 1029 8.3 3 1025 5 (8.3)(1025) 6.22 3 1029 5 (6.22)(1029) ( ) 5 (8.3)___ 1 105 5 (6.22)___ 1 109 5 (8.3)________ 1 100,000 ) 1 5 (6.22) _____________ 1,000,000,000 5 (8.3)(0.00001) 5 (6.22)(0.000000001) ( ( ) The number written in standard notation is The number written in standard notation is 0.000083. 0.00000000622. 27. 4.7 3 1023 28. 3.85 3 10212 4.7 3 1023 5 (4.7)(1023) © 2011 Carnegie Learning ( ) ( ) 5 (4.7)( 1 ) 1000 5 (4.7)___ 1 103 _____ 5 (4.7)(0.001) 3.85 3 10212 5 (3.85)(10212) ( ) 1 5 (3.85)( 1,000,000,000,000 ) 5 (3.85)____ 1 1012 _________________ 5 (3.85)(0.000000000001) The number written in standard notation is The number written in standard notation is 0.0047. 0.00000000000385. Chapter 13 Skills Practice • 901 Lesson 13.4 Skills Practice page 10 29. An oxygen atom has a radius of about 4.8 3 10211meters. 4.8 3 1011 5 (4.8)(10211) 2 ( ) 1 5 (4.8)( 100,000,000,000 ) 5 (4.8)____ 1 1011 ________________ 5 (4.8)(0.00000000001) The number written in standard notation is 0.000000000048. 30. The diameter of a white blood cell is about 1 3 1025meters. 1 3 1025 5 (1)(1025) ( ) 5 (1)___ 1 105 5 (1)________ 1 100,000 5 (1)(0.00001) ( ) © 2011 Carnegie Learning The number written in standard notation is 0.00001. 902 • Chapter 13 Skills Practice Lesson 13.4 Skills Practice page 11 Name_________________________________________________________ Date__________________________ 31. A nitrogen atom has a radius of about 5.6 3 10211meters. 5.6 3 10211 5 (5.6)(10211) ( ) 1 5 (5.6)( 100,000,000,000 ) 5 (5.6)____ 1 1011 ________________ 5 (5.6)(0.00000000001) The number written in standard notation is 0.000000000056. 32. The width of a human hair is about 1.8 3 1023centimeters. 1.8 3 1023 5 (1.8)(1023) ( ) 5 (1.8)(_____ 1 1000 ) 5 (1.8)___ 1 103 5 (1.8)(0.001) © 2011 Carnegie Learning The number written in standard notation is 0.0018. Chapter 13 Skills Practice • 903 © 2011 Carnegie Learning 904 • Chapter 13 Skills Practice Lesson 13.5 Skills Practice Name_________________________________________________________ Date__________________________ Are We There Yet? What Is the Distance? Operations with Scientific Notation Problem Set Calculate each product. Express the product in scientific notation. 2. (3 3 107)(2 3 105) 1. (4 3 103)(2 3 106) (4 3 103)(2 3 106) 5 (4)(2)(103)(106) (3 3 107)(2 3 105) 5 (3)(2)(107)(105) 5 (8)(10316 ) 5 (6)(10715 ) 5 8 3 109 5 6 3 1012 3. (8 3 106)(1 3 1023) 4. (2 3 1023)(3 3 108) (8 3 106)(1 3 1023) 5 (8)(1)(106)(1023) (2 3 1023)(3 3 108) 5 (2)(3)(1023)(108) 5 (8)(1061 (23)) 5 (6)(102318 ) 5 8 3 103 5 6 3 105 6. (7.9 3 103)(2.6 3 105) © 2011 Carnegie Learning 5. (3.7 3 104)(5.2 3 109) (3.7 3 104)(5.2 3 109) 5 (3.7)(5.2)(104)(109) (7.9 3 103)(2.6 3 105) 5 (7.9)(2.6)(103)(105) 5 (19.24)(10419 ) 5 (20.54)(10315 ) 5 19.24 3 1013 5 20.54 3 108 5 1.924 3 1014 5 2.054 3 109 Chapter 13 Skills Practice • 905 Lesson 13.5 Skills Practice page 2 8. (4.2 3 1024)(9.1 3 1026) 7. (2.8 3 1028)(6.31 3 104) (2.8 3 1028)(6.31 3 104) 5 (2.8)(6.31)(1028)(104) (4.2 3 1024)(9.1 3 1026) 5 (4.2)(9.1)(1024)(1026) 5 (17.668)(102814 ) 5 (38.22)(10241(26)) 5 17.668 3 1024 5 38.22 3 10210 5 1.7668 3 1023 5 3.822 3 1029 9. Seismosaurus is the longest known dinosaur. It measured 1800 inches. How far would 3000 Seismosaurus dinosaurs span if they were placed head to tail? Use scientific notation to calculate the length. 1800 5 1.8 3 103 3000 5 3 3 103 (1.8 3 103)(3 3 103) 5 (1.8)(3)(103)(103) 5 (5.4)(10313 ) 5 5.4 3 106 © 2011 Carnegie Learning The 3000 Seismosaurus dinosaurs would span 5.4 3 106 inches. 906 • Chapter 13 Skills Practice Lesson 13.5 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 10. According to many scientists, Argentinosaurus is the heaviest known dinosaur. It weighed 220,000 pounds. How much would 1500 Argentinosaurus dinosaurs weigh? Use scientific notation to calculate the weight. 220,000 5 2.2 3 105 1500 5 1.5 3 103 (2.2 3 105)(1.5 3 103) 5 (2.2)(1.5)(105)(103) 5 (3.3)(10513 ) 5 3.3 3 108 The 1500 Argentinosaurus dinosaurs would weigh 3.3 3 108 pounds. 11. The bee hummingbird is the world’s smallest bird. It is about 0.05842 meters long. How far would 2,000,000 bee hummingbirds span if they were placed head to tail? Use scientific notation to calculate the length. © 2011 Carnegie Learning 0.05842 5 5.842 3 1022 2,000,000 5 2 3 106 (5.842 3 1022)(2 3 106) 5 (5.842)(2)(1022)(106) 5 (11.684)(102216) 5 11.684 3 104 5 1.1684 3 105 The 2,000,000 bee hummingbirds would span 1.1684 3 105 meters. Chapter 13 Skills Practice • 907 Lesson 13.5 Skills Practice page 4 12. The pygmy shrew is the world’s smallest mammal by weight. It weighs just 0.0013 kilograms. How much would 3,000,000 pygmy shrews weigh? Use scientific notation to calculate the weight. 0.0013 5 1.3 3 1023 3,000,000 5 3 3 106 (1.3 3 1023)(3 3 106) 5 (1.3)(3)(1023)(106) 5 (3.9)(102316 ) 5 3.9 3 103 The 3,000,000 pygmy shrews would weigh 3.9 3 103 kilograms. Simplify each expression. Express the quotient in scientific notation. ( )( ) 5 (8 3 105) _________ 5 __ 8 ___ 10 2 102 (2 3 102) (12 3 108) 14. __________ (6 3 103) ) ( 6 )(10 (12 3 10 ) ___ __________ 12 ___ 103 3 5 8 (6 3 10 ) 8 5 (4)(10522) 5 (2)(10823) 5 (4)(103) 5 (2)(105) 5 4 3 103 5 2 3 105 908 • Chapter 13 Skills Practice © 2011 Carnegie Learning (8 3 105) 13. ________ (2 3 102) Lesson 13.5 Skills Practice page 5 Name_________________________________________________________ Date__________________________ (18 3 1022) 16. ___________ (3 3 1026) (15 3 1027) 15. ___________ (5 3 104) ( 5 )( 10 ) 27 (15 3 10 ) ___ ___________ 15 ____ 10 4 4 5 27 (5 3 10 ) 22 (3 3 10 ) 5 (3)(102724) 5 (6)(10222(26)) 5 (3)(10211) 5 (6)(104) 5 3 3 10211 5 6 3 104 (1.508 3 107) 17. ____________ (2.6 3 103) (5.92 3 106) 18. ___________ (3.7 3 104) ) ( 2.6 )(10 ( )( ) 7 (1.508 3 10 ) 1.508 ____________ ______ ___ 103 3 5 7 (2.6 3 10 ) © 2011 Carnegie Learning ) ( 3 )(10 22 (18 3 10 ) ___ ___________ 5 18 ____ 1026 26 (5.92 3 106) 5.92 106 ___ ___________ 5 _____ 4 3.7 104 (3.7 3 10 ) 5 (0.58)(10723) 5 (1.6)(10624) 5 (0.58)(104) 5 (1.6)(102) 5 5.8 3 103 5 1.6 3 102 (8.82 3 1027) 20. ____________ (2.52 3 1022) (3.68 3 1028) 19. ____________ (3.2 3 1024) ) ( 3.2 )(10 28 (3.68 3 10 ) _____ 3.68 ____________ ____ 1024 24 5 28 (3.2 3 10 ) )(10 ) (2.52 27 (8.82 3 10 ) _____ 8.82 ____________ ____ 1022 22 5 27 (2.52 3 10 ) 5 (1.15)(10282(24)) 5 (3.5)(10272(22)) 5 (1.15)(1024) 5 (3.5)(1025) 5 1.15 3 1024 5 3.5 3 1025 Chapter 13 Skills Practice • 909 Lesson 13.5 Skills Practice page 6 Simplify each expression. Express your answer in scientific notation. 21. (5.9 3 105)(4.8 3 103) 22. (7.83 3 103)(2.9 3 108) (5.9 3 105)(4.8 3 103) 5 (5.9)(4.8)(105)(103) (7.83 3 103)(2.9 3 108) 5 (7.83)(2.9)(103)(108) 5 (28.32)(10513) 5 (22.707)(10318) 5 28.32 3 108 5 22.707 3 1011 5 2.8 3 109 5 2.3 3 1012 24. (5.31 3 105)(6 3 1028) (2.90 3 1027)(4.860 3 1022) (5.31 3 105)(6 3 1028) 5 (5.31)(6)(105)(1028) 5 (2.90)(4.860)(1027)(1022) 5 (31.86)(1051(28)) 5 (14.094)(10271(22)) 5 31.86 3 1023 5 14.094 3 1029 5 3 3 1022 5 1.41 3 1028 (4.5 3 105) 25. __________ (3.8 3 102) )(10 ) (3.8 5 (4.5 3 10 ) ___ __________ 5 4.5 ___ 102 2 5 (3.8 3 10 ) (5.12 3 106) 26. ___________ (8 3 103) ( 8 )(10 ) 6 (5.12 3 10 ) _____ 5.12 ___________ 5 ___ 10 6 (8 3 10 ) 3 3 5 (1.184210 . . . )(10522) 5 (0.64)(10623) 5 (1.184210 . . . )(103) 5 0.64 3 103 5 1.2 3 103 5 6 3 102 910 • Chapter 13 Skills Practice © 2011 Carnegie Learning 23. (2.90 3 1027)(4.860 3 1022) Lesson 13.5 Skills Practice page 7 Name_________________________________________________________ Date__________________________ 27. A football is about 280 millimeters long. A football field is about 100,000 millimeters long. How many footballs placed end to end would be needed to span the field? Use scientific notation to calculate the number of footballs. 280 5 2.8 3 102 100,000 5 1 3 105 )(10 ) (2.8 5 ( ___ 1 ( 10 2.8 ) 5 05) ___________ (1 3 1 1 ___ 102 5 ___ (2.8 3 102) 522 ) 5 (0.357142 . . . )(103) 5 4 3 102 5 400 © 2011 Carnegie Learning About 400 footballs would span the football field. Chapter 13 Skills Practice • 911 Lesson 13.5 Skills Practice page 8 28. A large Siberian tiger can weigh up to 305,000 grams. A small Sand cat can weigh as little as 1500 grams. How many times greater is the weight of a Siberian tiger than the weight of a Sand cat? Use scientific notation to calculate the difference in weight. 305,000 5 3.05 3 105 1500 5 1.5 3 103 ) ( 1.5 )(10 5 (3.05 3 10 ) _____ ___________ 5 3.05 ___ 103 3 5 (1.5 3 10 ) __ 5 (2.03 )(10 523) 5 (2.03 )(10 2) 5 2.0 3 102 5 200 __ © 2011 Carnegie Learning The weight of a Siberian tiger is about 200 times greater than the weight of a Sand cat. 912 • Chapter 13 Skills Practice Lesson 13.6 Skills Practice Name_________________________________________________________ Date__________________________ Watch Your Step! Identifying the Properties of Powers Problem Set Justify each step to simplify the expression. Choose the properties from the box. Product Rule Power to a Negative Quotient Rule of Powers Power Rule Exponent Rule of Powers Zero Power Simplify Powers Identity Commutative Rule Property of Property of Multiplication Multiplication 1. 4x5 6x2 y6 xy 4x5 6x2 y6 xy 5 (4 6)(x5 x2 x)( y6 y) Commutative Property of Multiplication 5 (24)(x51211 )( y611 ) Product Rule of Powers 5 24x8y7 Simplify Powers © 2011 Carnegie Learning 2. 3a2 b3 7ab5 b2 3a2 b3 7ab5 b2 5 (3 7)(a2 a)(b3 b5 b2 ) Commutative Property of Multiplication 5 (21)(a211 )(b31512 ) Product Rule of Powers 5 21a3b10 Simplify Powers Chapter 13 Skills Practice • 913 Lesson 13.6 Skills Practice page 2 3. (4m2 n5)3 (4m2 n5 )3 5 43 (m)23(n)53 Power to a Power Rule 5 64m6n15 Simplify Powers 4. (23x7 y3)5 (23x7 y3 )5 5 (23)5(x)75( y)35 Power to a Power Rule 5 2243x35y15 Simplify Powers 27y8 z5 5. _______ 4 2 23y z ( )( ) ( ) 5 29( y824 )(z522 ) Quotient Rule of Powers 5 29y4z3 Simplify Powers 296m9 n2 6. _________ 8m2 n6 ( )( ) ( ) 9 2 2 296m9n 5 _________ _____ 296 ___ m2 __ n6 Commutative Property of Multiplication 2 6 8 m n 8m n 5 212(m922)(n226) Quotient Rule of Powers 5 212m7 n24 Simplify Powers m 5 _______ 212 4 n Negative Exponent Rule 7 914 • Chapter 13 Skills Practice © 2011 Carnegie Learning y8 z5 27y8 z5 27 __ _______ 4 ___ Commutative Property of Multiplication 4 2 5 ___ 23y z 23 y z2 Lesson 13.6 Skills Practice page 3 Name_________________________________________________________ Date__________________________ 7. 22x5y3 8x2y25 x29 y2 22x5y3 8x2y25 x29y2 5 (22 8)(x5x2x29)( y3y25y2) Commutative Property of Multiplication 5 (216)(x5121(29) )( y31(25)12 ) Product Rule of Powers 5 216x22 y0 Simplify Powers 5 216x22(1) Zero Power Rule 216 5 _____ Negative Exponent Rule x 2 m n 8. _____________ 42m n6 5 6m n 5 3 4 2 Commutative Property of Multiplication ( 6 )( m ) ( n ) 5 (7)( m n Product Rule of Powers m )( n ) 5 3 4 2 5 4 3 2 n ___ _____________ 5 42 _____ m m ____ n n 42m n 6 m 5 6 6m n © 2011 Carnegie Learning 5 514 312 _____ ____ 5 6 5 (7)(m51426 )(n31225 ) Quotient Rule of Powers 5 7m3 n0 Simplify Powers 5 7m3 (1) Zero Power Rule 5 7m3 Identity Property of Multiplication Chapter 13 Skills Practice • 915 Lesson 13.6 Skills Practice page 4 Choose which solution is correct. c. b. 9. a. 3x 4x 5 (3 4)(x x ) 2 3 2 3 3x 4x 5 (3 4)(x x ) 2 3 2 3 3x2 4x35 (3 4)(x2x3) 5 (12)(x213) 5 (12)(x223) 5 (12)(x23 ) 5 (12)(x5) 5 (12)(x21) 5 (12)(x6) 5 12x5 12 5 ___ x 5 12x6 The correct solution is a. 10. a. b. 25a 2a 6 3 c. 25a 2a 6 25a6 2a3 3 5 (25 2)(a6a3 ) 5 (25 2)(a6a3 ) 5 (25 2)(a6a3 ) 5 (210)(a623) 5 (210)(a63) 5 (210)(a613) 5 (210)(a3) 5 (210)(a18) 5 (210)(a9) 5 210a3 5 210a18 5 210a9 The correct solution is c. ( 4 )( m) c. ( 4 )( m) 36 m 36m ___ ______ 5 ____ 36m ___ 36 m ______ 5 ____ 36 m 36m ___ ______ 5 ____ 5 (9)(m1244) 5 (9)(m1224) 5 (9)(m1214) 5 (9)(m3) 5 (9)(m8) 5 (9)(m16) 5 9m3 5 9m8 5 9m16 12 4m 4 ( 4 )( m) b. 12 4 12 4m 4 The correct solution is b. 916 • Chapter 13 Skills Practice 12 4 12 4m 4 12 4 © 2011 Carnegie Learning 11. a. Lesson 13.6 Skills Practice page 5 Name_________________________________________________________ Date__________________________ 12. a. b. ( 5 )( x) 60x2 ___ 60 x2 ____ 5 __ 5x8 8 c. 60x ___ 60 x ____ 5 __ x 60 x 5 ( 60 5x ) ( 5 )(x ) ( 5 )( x) 2 2 2 5x8 ____ 8 8 2 ___ __ 8 5 (12)(x822) 5 (12)(x218) 5 (12)(x228) 5 (12)(x6) 5 (12)(x10) 5 (12)(x26) 5 12x6 5 12x10 12 5 ___ 6 x The correct solution is c. 13. a. b. (5x ) 5 (5) (x ) 2 3 3 2 3 c. (5x ) 5 (5) (x ) 2 3 3 2 3 (5x2)3 5 (5)3(x2)3 3 5 (125)(x23) 5 (125)(x213) 5 (125)(x2 ) 5 (125)(x6) 5 (125)(x5) 5 (125)(x8) 5 125x6 5 125x5 5 125x8 The correct solution is a. 14. a. (4y ) 5 (4) ( y ) © 2011 Carnegie Learning c. b. 23 3 3 23 3 (4y ) 5 (4) ( y ) 23 3 3 23 3 (4y23)3 5 (4)3( y23)3 5 (64)( y2313) 5 (64)( y233) 5 (64)( y2323) 5 (64)( y0) 5 (64)( y29) 5 (64)( y26) 5 (64)(1) 5 ___ 64 y9 64 5 ___ y6 5 64 The correct solution is b. Chapter 13 Skills Practice • 917 Lesson 13.6 Skills Practice page 6 Simplify each expression. Show your work. 15. 12x4y3 3x2y25 2a7b22 16. 17a25b23 12x4y3 3x2y25 5 (12 3)(x4x2)( y3y25) 17a25b23 2a7b22 5 (17 2)(a25a7)(b23b22) 5 (36)(x412)( y31(25)) 5 (34)(a2517)(b231(22)) 5 (36)(x6)( y22) 5 (34)(a2)(b25) 36x 6 5 _____ y2 34a 2 5 _____ b5 18. (2a5b2c3)5 17. (23x4y23)2 (23x4y23)2 5 (23)2(x4)2( y23)2 (2a5b2c3)5 5 (2)5(a5)5(b2)5(c3)5 5 (9)(x)42( y)232 5 (32)(a)55 (b)25 (c)35 5 9x8y26 5 32a25b10c15 9x 5 ___ y6 8 )(m )(n ) (14 3 5 3 5 _______ 28 ___ m7 __ n2 28m7 n 5 ___ 2 14m n 35x8y6 20. ______ 5 3 7x y ( 7 )(x )(y ) 8 y 35x y ___ _______ 35 __ x __ 5 8 6 7x5 y3 6 5 3 5 (2)(m327)(n522) 5 (5)(x825)( y623) 5 (2)(m24)(n3) 5 5x3y3 2n3 5 ____ m4 918 • Chapter 13 Skills Practice © 2011 Carnegie Learning 28m3 n5 19. _______ 7 2 14m n Lesson 13.6 Skills Practice page 7 Name_________________________________________________________ Date__________________________ a b 22. ____________ 3a b7 4 6a b9 4 21. (2x5y3)2 x2 y4 (2x5y3)2 x2 y4 5 (2)2 (x5)2( y3)2 x2 y4 5 3 ( 6 )( a )( b ) 5 (___ 126 ) (____ aa ) (____ bb ) 4 5 4 5 a3 b2 _____ a3 b2 4 ____________ 3a b 4 3 ______ a ______ b 5 6a7 b9 7 5 (4)(x) ( y) x y 52 32 2 4 5 (4)(x )( y ) x y 10 6 2 4 413 512 7 9 ( )( ) 7 7 5 2__ a7 __ b9 a b 5 2(a727)(b729) 5 2(a0)(b22) 5 2(1)(b22) 2 5 __ b2 5 4x12y10 (4m3 n2)4 23. ________ 8m5 5x2 y4 6x4 y 24. __________ 10x3 y3 (4)4(m3)4(n2)4 (4m3n2)4 ___________ 5 ________ 5 8m 8m5 © 2011 Carnegie Learning 9 5 4(x1012)( y614) 2 (256)(m)3 ? 4(n2 ? 4) 5 ______________ 8m5 (256)m12n8 5 __________ 8m5 ( )( ) 12 (n8 ) 5 ____ 256 ____ m 8 m5 5 (32)(m1225)(n8) ( 10 )( x )( y 10x y y 5 ( 30 ) ( x ) 10 x (y ) y 5 3( x ) ( ) x y ) y y 5x y 6x y ____ 56 ______ x ___________ 5 x 3 _____ 3 3 3 2 4 4 2 214 4 4 411 ___ _________ 3 3 6 5 3 3 __ __ 5 3(x623)( y523) 5 3x3y2 5 32m7n8 Chapter 13 Skills Practice • 919 © 2011 Carnegie Learning 920 • Chapter 13 Skills Practice