88 Chapter 4 Exponential Functions Homework 4.1 1.1. 1122= negative integer exponent 3. 221 139 3= = negative integer exponent 5. ( ) ( )( )24 4 4 16 = = 7. 1 11 12 3negative integer exponents2 33 2 56 6 6 + = += + = 9. 902902 900 290077 7 497= = = 11. ( ) 2003 2000 2003 2000 34 4 4 4 64+ = = = 13. ( )03 5 225 411 89 1 + = 15. 7 9 7 9 16b b b b+= = 17. ( ) 5 5 5 5 01 b b b b+ = = = 19. ( )( ) ( ) ( )( )7 6 7 67 6 13 2 3 26 66 6or b b b bb bb b + = = = = 21. ( ) ( )( )4 442 2 2 4 81 1 b b b b = = 23. ( )( )( )( )( )( ) ( ) ( )( ) ( )5 24 2 3 45 5 2 25 24 2 3 43 2 4 2 4 5 2 5220 10 6 820 6 10 82 32 3132313291329b c b cb c b cb c b cb c b cb b c c === = 26 22621329329b cbc = = 25. 1010 15 515 51 bb bb b = = = 27. ( )1212 9 12 9 39 32 22 2 2bb b bb b + = = = = 29. 5 5 5 4 5 5 1 04 512 6 6 67 7 7 14b c b c b c bb c = = = 31. ( ) 7 6 7 3 8 3 2 8 82 6 81 5 05153 45313b c d b c dc b db c dbc = == 33. ( )( )( ) ( )3 4 5 13 5 4 12 17 2 178 32 178 2 3 1710 1410 145 42080 8044414b c b cb cb c b cb cb cb cb cb c + + == = = = 35. ( )( )( )( )( ) ( )( )( )3 6 1 23 1 6 22 5 2 4 5 4 12 83 52 3 8 55 1351324 4924 4928 14 28 143332b c b cb cb c b c b cb cb cb cb cbc + ++ + ===== SSM: Intermediate AlgebraHomework 4.289 37. ( )( )35 23 5 3 2 33 315 6315 3 6 118 7187337 7277277277277b cb cb c b cb cb cb cb cbc ===== 39. ( )( )25 225 2 2 42 423 63 2 6 26 12612b cb cb cb cb cb cbc = ==== 41. 04 72 35167b cb c = 43. 4 44 5 4 2 4 4 2 4 16 87 2 7 5 4 7 4 5 4 28 20714 2 2 16b c b c b c b cb c b c b c b c = = = 45. 1 11b cbc = 47. 1 11 1b cb c + = + 49. 4 3 4 3 7 n n n n nb b b b+= = 51. ( ) ( )7 17 1 2 3 7 1 2 3 5 42 3nn n n n nnbb b bb + += = = 53.Student B is correct.Student A did not distribute the 1 exponent to the base 5 correctly.It should have been 15 and not 5.Student A mistakenly multiplied 5 by 1. 55. 22 4 = ( ) 2 1 2 = 21 12 4 = 12 1122=11 222 1 = = ( )22 4 =22 4 =The ties are 1122=and( )222 2 = . 57.a. 0 0 0 0 05 4 3 2 1 1 = = = = = It is reasonable to assume that 00 1 = , also. b. 5 4 3 2 10 0 0 0 0 0 = = = = = It is reasonable to assume that 00 0 = , also. c.Answers may vary.It is a good idea to leave 00meaningless, since depending on the reasoning used, we get different values for 00 . 59.a. 11bb= b. ( )( )11 1 1b b b = = c. ( )( )( )( )111 1 1 1 11b b bb = = = d. ( )( )( )( )( )1111 1 1 1 1b b b = = e.If there are n exponents, 1 will be multiplied by itself n times.If n is even, the resulting exponent will be 1 and the answer will be b.If n is odd, the resulting exponent will be -1 and the answer is 1b. 61.Answers may vary. Homework 4.2 1.1. 1/ 216 4 = , since 24 16 = . 3. 1/ 31000 10 = , since 310 1000 = . Homework 4.2SSM: Intermediate Algebra 90 5. 1/ 249 7 = , since 27 49 = . 7. 1/ 3125 5 = , since 35 125 = . 9. ( )44/ 3 1/ 3 48 8 2 16 = = = 11. ( )33/ 2 1/ 2 39 9 3 27 = = = 13. ( )22/ 5 1/ 5 232 32 2 4 = = = 15. ( )55/ 2 1/ 2 54 4 2 32 = = = 17. 1/ 31/ 31 1273 27= = 19. 1/ 21/ 21 1366 36 = = 21. ( )5/ 25/ 2 5 51/ 21 1 1 1432 4 24= = = = 23. ( )( )( )( )( )4/ 34/ 341/ 34127271271 1813 === = 25. 1 3 1 3 414 4 4 4 42 2 2 2 2 2+= = = = 27. ( )( )21121 223 3 3 3 = = = 29. 11 5 632 3 3 35377 7 7 497 = = = = 31. 7 5 7 5 1226 6 6 6 6bb b b b+= = = 33. 23 13 3 13 102 5 5 5 5 51bbb b b b + = = = =35. ( ) ( ) ( )18 1/ 4 1/ 41/ 48 8 2 416 16 2 2 b b b b = = = 37. ( )( )( ) ( ) ( )( )( )1/ 28 141/ 28 141/ 2 1/ 21/ 28 141 18 142 24 744 25254254545b cb cb cb cb c ==== 39. ( )( )1 7 3 23/ 5 1/ 4 2/ 5 7/ 44 4 5 55 85 41 22b c b c b cbcb cbc + + ==== 41. ( ) ( ) ( )( )1 41/ 5 4/ 55 5555 5 55 5bcd bcd bcdbcd bcd+== = 43. ( ) ( )( ) ( ) ( ) ( ) ( ) ( )( )1/ 3 1/ 26 9 20 41/ 3 1/ 3 1/ 2 1/ 21/ 3 1/ 26 9 20 42 3 10 22 10 3 22 10 3 212 58 168 162 42 488b c b cb c b cb c b cb b c cb cb c+ +===== 45. ( )5.6 3.85.6 2.3 3.8 1.32.3 1.33.3 2.53.32.5b cb cb cb cbc === 47. ( ) ( )( ) ( )1/ 2 1/ 23 2 3 55 2 2 21/ 23 52 21/ 2841/ 21/ 28 41/ 2 21/ 249 925 259259259 3525b c b bb c c cbcbcb bcc++ = = = = = 49. 3 2 15 143/ 7 2/ 5 29/ 357 5 35 35b b b b b+ += = =SSM: Intermediate AlgebraHomework 4.291 51. 5 1 10 3 5/ 67 /126 4 12 121/ 4bb b bb = = = 53. ( ) ( )( )( )3/ 2 3/ 22/ 3 2/ 34/ 5 4/ 53/ 23/ 22/ 33/ 24/ 531/ 26/ 561351/ 51/ 58 4244288b bb bbbbbbbb = ==== = 55. ( )( )( ) ( )( ) ( )1/ 3 1/ 31/ 33 1/ 3 31/ 4 1/ 41/ 43 1/ 4 31/ 31/ 4 3/ 41 1 313 4 44 3 112 12 41/12 1/ 48 881 8123232323bc b cbc b cb cb cb cb cb c ===== 57. 23.965 10 3.965 100396.5 = = 59. 112.39 10 2.39102.39100.239 = == 61. 25.2 10 5.2 100520 = = 63. 519.113 10 9.113100, 0000.00009113 = = 65. 56.52 10 6.52 100, 000652, 000 = = 67. 59 10 9 100, 000 900, 000 = = 69. 218 10 810081000.08 = = = 71. 35246 5.246 1000 5.246 10 = = 73. 423, 587 2.3587 10, 000 2.3587 10 = = 75. 49.80.00098 9.8 1010, 000= = 77. 53.460.0000346 3.46 10100, 000= = 79. 442, 215 4.2215 10, 000 4.2215 10 = = 81. 38.9280.008928 8.928 101000 = = 83. 08.0 8.0 10 = 85. 5100, 000 1.0 100, 000 1 10 = = 87. 82.87 10 2.87 100, 000, 000 287, 000, 000 = = 89. 86.36.3 10 0.000000063100, 000, 000 = = 91. 12 1210 1 1011, 000, 000, 000, 0000.000000000001 = == 93. 5830, 000 8.3 100, 000 8.3 10 = = 95. 74.70.00000047 4.7 1010, 000, 000= = 97. Answers may vary.1/ 25is some number whose square is 5. 5is also some number whose square is 5.Since 1/ 25and5both equal 5, 1/ 25=5 . 99.Answers may vary. Homework 4.3SSM: Intermediate Algebra 92 Homework 4.3 1.1. 3xy = 3. 10xy = 5. ( ) 3 2xy = 7. ( ) 6 3xy = 9. 1153xy = 11. 1122xy = 13. ( ) ( ) 2 , 2x xf x g x = = 15. ( ) ( ) ( ) ( ) 4 3 , 4 3x xf x g x = = SSM: Intermediate AlgebraHomework 4.393 17. ( ) ( )1 18 , 82 2x xf x g x = = 19.a.0 and1 a b < >negative output and exponential growth b.0 and1 a b > >positive output and exponential growth c.0 and 0 1 a b >