Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Intermediate Algebra
In the following exercises, simplify using absolute values as necessary. 39. (a) 49x2 (b) 81x18In the following exercises, simplify using absolute values as necessary. 40. (a) 100y2 (b) 100m32In the following exercises, simplify using absolute values as necessary. 41. (a) 121m20 (b) 64a2In the following exercises, simplify using absolute values as necessary. 42. (a) 81x36 (b) 25x2In the following exercises, simplify using absolute values as necessary. 43. (a) 16x84 (b) 64y126In the following exercises, simplify using absolute values as necessary. 44. (a) 8c93 (b) 125d153In the following exercises, simplify using absolute values as necessary. 45. (a) 216a63 (b) 32b205In the following exercises, simplify using absolute values as necessary. 46. (a) 128r147 (b) 81s244In the following exercises, simplify using absolute values as necessary. 47. (a) 144x2y2 (b) 169w8y10 (c) 8a51b63In the following exercises, simplify using absolute values as necessary. 48. (a) 196a2b2 (b) 81p24q6 (c) 27p45q93In the following exercises, simplify using absolute values as necessary. 49. (a) 121a2b2 (b) 9c8d12 (c) 64x15y663In the following exercises, simplify using absolute values as necessary. 50. (a) 225x2y2z2 (b) 36r6s20 (c) 125y18z273Why is there no real number equal to 64 ?What is the difference between 92 and 9 ?Explain what is meant by the nthroot of a number.Explain the difference of finding the nthroot of a number when the index is even compared to when the index is odd.Simplify: 48 .Simplify: 45 .Simplify: (a) 288 (b) 813 (c) 644 .Simplify: (a) 432 (b) 6253 (c) 7294 .Simplify: (a) b5 (b) y64 (c) z53 .Simplify: (a) p9 (b) y85 (c) q136 .Simplify: (a) 32y5 (b) 54p103 (c) 64q104 .Simplify: (a) 75a9 (b) 128m113 (c) 162n74 .Simplify: (a) 98a7b5 (b) 56x5y43 (c) 32x5y84 .Simplify: (a) 180m9n11 (b) 72x6y53 (c) 80x7y44 .Simplify: (a) 643 (b) 814 .Simplify: (a) 6253 (b) 3244 .Simplify: (a) 5+75 (b) 10755 .Simplify: (a) 2+98 (b) 6453 .Simplify: (a) 7548(b) 542503(c) 321624.Simplify: (a) 98162 (b) 243753 (c) 43244 .Simplify: (a) a8a6 (b) x7x34 (c) y 17y54 .Simplify: (a) x 14x 10 (b) m 13m73 (c) n 12n25 .Simplify: 24p349 .Simplify: 48x5100 .Simplify: (a) 80m3n6 (b) 108c 10d63 (c) 80x 10y44 .Simplify: (a) 54u7v8 (b) 40r3s63 (c) 162m 14n 124 .Simplify: (a) 54x5y372x4y (b) 16x5y754x2y23 (c) 5a8b680a3b24 .Simplify: (a) 48m7n2100m5n8 (b) 54x7y5250x2y23 (c) 32a9b7162a3b34 .Simplify: (a) 98z52z (b) 500323 (c) 486m 1143m54 .Simplify: (a) 128m92m (b) 192333 (c) 324n742n34 .In the following exercises, use the Product Property to simplify radical expressions. 55. 27In the following exercises, use the Product Property to simplify radical expressions. 56. 80In the following exercises, use the Product Property to simplify radical expressions. 57. 125In the following exercises, use the Product Property to simplify radical expressions. 58. 96In the following exercises, use the Product Property to simplify radical expressions. 59. 147In the following exercises, use the Product Property to simplify radical expressions. 60. 450In the following exercises, use the Product Property to simplify radical expressions. 61. 800In the following exercises, use the Product Property to simplify radical expressions. 62. 675In the following exercises, use the Product Property to simplify radical expressions. 63. (a) 324 (b) 645In the following exercises, use the Product Property to simplify radical expressions. 64. (a) 6253 (b) 1286In the following exercises, use the Product Property to simplify radical expressions. 65. (a) 645 (b) 2563In the following exercises, use the Product Property to simplify radical expressions. 66. (a) 31254 (b) 813In the following exercises, simplify using absolute value signs as needed. 67. (a) y11 (b) r53 (c) s104In the following exercises, simplify using absolute value signs as needed. 68. (a) m13 (b) u75 (c) v116In the following exercises, simplify using absolute value signs as needed. 69. (a) n21 (b) q83 (c) n108In the following exercises, simplify using absolute value signs as needed. 70. (a) r25 (b) p85 (c) m54In the following exercises, simplify using absolute value signs as needed. 71. (a) 125r13 (b) 108x53 (c) 48y64In the following exercises, simplify using absolute value signs as needed. 72. (a) 80s15 (b) 96a75 (c) 128b76In the following exercises, simplify using absolute value signs as needed. 73. (a) 242m23 (b) 405m104 (c) 160n85In the following exercises, simplify using absolute value signs as needed. 74. (a) 175n13 (b) 512p55 (c) 324q74In the following exercises, simplify using absolute value signs as needed. 75. (a) 147m7n11 (b) 48x6y73 (c) 32x5y44In the following exercises, simplify using absolute value signs as needed. 76. (a) 96r3s3 (b) 80x7y63 (c) 80x8y94In the following exercises, simplify using absolute value signs as needed. 77. (a) 192q3r7 (b) 54m9n103 (c) 81a9b84In the following exercises, simplify using absolute value signs as needed. 78. (a) 150m9n3 (b) 81p7q83 (c) 162c11d124In the following exercises, simplify using absolute value signs as needed. 79. (a) 8643 (b) 2564In the following exercises, simplify using absolute value signs as needed. 80. (a) 4865 (b) 646In the following exercises, simplify using absolute value signs as needed. 81. (a) 325 (b) 18In the following exercises, simplify using absolute value signs as needed. 82. (a) 83 (b) 164In the following exercises, simplify using absolute value signs as needed. 83. (a) 5+12 (b) 10242In the following exercises, simplify using absolute value signs as needed. 84. (a) 8+96 (b) 8804In the following exercises, simplify using absolute value signs as needed. 85. (a) 1+45 (b) 3+903In the following exercises, simplify using absolute value signs as needed. 86. (a) 3+125 (b) 15+755In the following exercises, use the Quotient Property to simplify square roots. 87. (a) 4580 (b) 8273 (c) 1814In the following exercises, use the Quotient Property to simplify square roots. 88. (a) 7298 (b) 24813 (c) 6964In the following exercises, use the Quotient Property to simplify square roots. 89. (a) 10036 (b) 813753 (c) 12564In the following exercises, use the Quotient Property to simplify square roots. 90. (a) 12116 (b) 162503 (c) 321624In the following exercises, use the Quotient Property to simplify square roots. 91. (a) x 10x6 (b) p 11p23 (c) q 17q 134In the following exercises, use the Quotient Property to simplify square roots. 92. (a) p 20p 10 (b) d 12d75 (c) m 12m48In the following exercises, use the Quotient Property to simplify square roots. 93. (a) y4y8 (b) u 21u 115 (c) v 30v 126In the following exercises, use the Quotient Property to simplify square roots. 94. (a) q8q 14 (b) r 14r53 (c) c 21c94In the following exercises, use the Quotient Property to simplify square roots. 95. 96x7121In the following exercises, use the Quotient Property to simplify square roots. 96. 108y449In the following exercises, use the Quotient Property to simplify square roots. 97. 300m564In the following exercises, use the Quotient Property to simplify square roots. 98. 125n7169In the following exercises, use the Quotient Property to simplify square roots. 99. 98r5100In the following exercises, use the Quotient Property to simplify square roots. 100. 180s 10144In the following exercises, use the Quotient Property to simplify square roots. 101. 28q6225In the following exercises, use the Quotient Property to simplify square roots. 102. 150r3256In the following exercises, use the Quotient Property to simplify square roots. 103. (a) 75r9s8 (b) 54a8b33 (c) 64c5d44In the following exercises, use the Quotient Property to simplify square roots. 104. (a) 72x5y6 (b) 96r 11s55 (c) 128u7v 126In the following exercises, use the Quotient Property to simplify square roots. 105. (a) 28p7q2 (b) 81s8t33 (c) 64p 15q 124In the following exercises, use the Quotient Property to simplify square roots. 106. (a) 45r3s 10 (b) 625u 10v33 (c) 729c 21d84In the following exercises, use the Quotient Property to simplify square roots. 107. (a) 32x5y318x3y (b) 5x6y940x5y33 (c) 5a8b680a3b24In the following exercises, use the Quotient Property to simplify square roots. 108. (a) 75r6s848rs4 (b) 24x8y481x2y3 (c) 32m9n2162mn24In the following exercises, use the Quotient Property to simplify square roots. 109. (a) 27p2q108p4q3 (b) 16c5d7250c2d23 (c) 2m9n7128m3n6In the following exercises, use the Quotient Property to simplify square roots. 110. (a) 50r5s2128r2s6 (b) 24m9n7375m4n3 (c) 81m2n8256m1n24In the following exercises, use the Quotient Property to simplify square roots. 111. (a) 45p95q2 (b) 64424 (c) 128x852x25In the following exercises, use the Quotient Property to simplify square roots. 112. (a) 80q55q (b) 625353 (c) 80m745m4In the following exercises, use the Quotient Property to simplify square roots. 113. (a) 50m72m (b) 125023 (c) 486y92y34In the following exercises, use the Quotient Property to simplify square roots. 114. (a) 72n 112n (b) 16263 (c) 160r 105r34Explain why x4=x2 . Then explain why x16=x8 .Explain why 7+9 is not equal to 7+9 .Explain how you know that x105=x2 .Explain why 644 is not a real number but 643 is.Write as a radical expression: (a) t12 (b) m13 (c) r14 .Write as a radical expression: (a) b16 (b) z15 (c) p14 .Write with a rational exponent: (a) 10m (b) 3n5 (c) 36y4 .Write with a rational exponent: (a) 3k7 (b) 5j4 (c) 82a3 .Simplify: (a) 3612 (b) 813 (c) 1614 .Simplify: (a) 10012 (b) 2713 (c) 8114 .Simplify: (a) (64)12 (b) 6412 (c) (64)12 .Simplify: (a) (256)14 (b) 25614 (c) (256)14 .Write with a rational exponent: (a) x5 (b) ( 3y4)3 (c) ( 2m 3n )5 .Write with a rational exponent: (a) a25 (b) ( 5ab3)5 (c) ( 7xy z )3 .Simplify: (a) 2723 (b) 8132 (c) 1634 .Simplify: (a) 432 (b) 2723 (c) 62534 .Simplify: (a) 1632 (b) 1632 (c) (16)32 .Simplify: (a) 8132 (b) 8132 (c) (81)32 .Simplify: (a) x16x13 (b) (x6)43 (c) x23x53 .Simplify: (a) y34y58 (b) (m9)29 (c) d15d65 .Simplify: (a) (32x 1 3 )35 (b) (x 3 4 y 1 2 )23 .Simplify: (a) (81n 2 5 )32 (b) (a 3 2 b 1 2 )43 .Simplify: (a) m23m13m53 (b) ( 25 m 1 6 n 11 6 m 2 3 n 1 6 )12 .Simplify: (a) u45u25u 135 (b) ( 27 x 4 5 y 1 6 x 1 5 y 5 6 )13 .In the following exercises, write as a radical expression. 119. (a) x12 (b) y13 (c) z14In the following exercises, write as a radical expression. 120. (a) r12 (b) s13 (c) t14In the following exercises, write as a radical expression. 121. (a) u15 (b) v19 (c) w120In the following exercises, write as a radical expression. 122. (a) g17 (b) h15 (c) j125In the following exercises, write with a rational exponent. 123. (a) x7 (b) y9 (c) f5In the following exercises, write with a rational exponent. 124. (a) r8 (b) s10 (c) t4In the following exercises, write with a rational exponent. 125. (a) 7c3 (b) 12d7 (c) 26b4In the following exercises, write with a rational exponent. 126. (a) 5x4 (b) 9y8 (c) 73z5In the following exercises, write with a rational exponent. 127. (a) 21p (b) 8q4 (c) 436r6In the following exercises, write with a rational exponent. 128. (a) 25a3 (b) 3b (c) 40c8In the following exercises, simplify. 129. (a) 8112 (b) 12513 (c) 6412In the following exercises, simplify. 130. (a) 62514 (b) 24315 (c) 3215In the following exercises, simplify. 131. (a) 1614 (b) 1612 (c) 62514In the following exercises, simplify. 132. (a) 6413 (b) 3215 (c) 8114In the following exercises, simplify. 133. (a) (216)13 (b) 21613 (c) (216)13In the following exercises, simplify. 134. (a) (1000)13 (b) 100013 (c) (1000)13In the following exercises, simplify. 135. (a) (81)14 (b) 8114 (c) (81)14In the following exercises, simplify. 136. (a) (49)12 (b) 4912 (c) (49)12In the following exercises, simplify. 137. (a) (36)12 (b) 3612 (c) (36)12In the following exercises, simplify. 138. (a) (16)14 (b) 1614 (c) 1614In the following exercises, simplify. 139. (a) (100)12 (b) 10012 (c) (100)12In the following exercises, simplify. 140. (a) (32)15 (b) (243)15 (c) 12513In the following exercises, write with a rational exponent. 141. (a) m5 (b) ( 3y3)7 (c) ( 4x 5y )35In the following exercises, write with a rational exponent. 142. (a) r74 (b) ( 2pq5)3 (c) ( 12m 7n )34In the following exercises, write with a rational exponent. 143. (a) u25 (b) ( 6x3)5 (c) ( 18a 5b )74In the following exercises, write with a rational exponent. 144. (a) a3 (b) ( 21v4)3 (c) ( 2xy 5z )24In the following exercises, simplify. 145. (a) 6452 (b) 8132 (c) (27)23In the following exercises, simplify. 146. (a) 2532 (b) 932 (c) (64)23In the following exercises, simplify. 147. (a) 3225 (b) 2723 (c) (25)12In the following exercises, simplify. 148. (a) 10032 (b) 4952 (c) (100)32In the following exercises, simplify. 149. (a) 932 (b) 932 (c) (9)32In the following exercises, simplify. 150. (a) 6432 (b) 6432 (c) (64)32In the following exercises, simplify. 151. (a) c14c58 (b) (p 12)34 (c) r45r95In the following exercises, simplify. 152. (a) 652612 (b) (b 15)35 (c) w27w97In the following exercises, simplify. 153. (a) y12y34 (b) (x 12)23 (c) m58m 138In the following exercises, simplify. 154. (a) q23q56 (b) (h6)43 (c) n35n85In the following exercises, simplify. 155. (a) (27q 3 2 )43 (b) (a 1 3 b 2 3 )32In the following exercises, simplify. 156. (a) (64s 3 7 )16 (b) (m 4 3 n 1 2 )34In the following exercises, simplify. 157. (a) (16u 1 3 )34 (b) (4p 1 3 q 1 2 )32In the following exercises, simplify. 158. (a) (625n 8 3 )34 (b) (9x 2 5 y 3 5 )52In the following exercises, simplify. 159. (a) r52r12r32 (b) ( 36 s 1 5 t 3 2 s 9 5 t 1 2 )12In the following exercises, simplify. 160. (a) a34a14a 104 (b) ( 27 b 2 3 c 5 2 b 7 3 c 1 2 )13In the following exercises, simplify. 161. (a) c53c13c23 (b) ( 8 x 5 3 y 1 2 27 x 4 3 y 5 2 )13In the following exercises, simplify. 162. (a) m74m54m24 (b) ( 16 m 1 5 n 3 2 81 m 9 5 n 1 2 )14Show two different algebraic methods to simplify 432 . Explain all your steps.Explain why the expression (16)32 cannot be evaluated.Simplify: (a) 8292 (b) 4x3+7x3 (c) 3x45y4.Simplify: (a) 5393 (b) 5y3+3y3 (c) 5m42m3.Simplify: (a) 7x77x+47x (b) 45xy4+25xy475xy4.Simplify: (a) 43y73y+23y (b) 67mn3+7mn347mn3.Simplify: (a) 18+62 (b) 616322503 (c) 2381312243.Simplify: (a) 27+43 (b) 4537403 (c) 12128353543.Simplify: (a) 32m750m7 (b) 135x7340x73.Simplify: (a) 27p348p3 (b) 256y5332n53.Simplify: (a) (32)(230) (b) (2183)(363).Simplify: (a) (33)(36) (b) (493)(363).Simplify: (a) (66x2)(830x4) (b) (412y34)(8y34).Simplify: (a) (26y4)(1230y) (b) (49a34)(327a24).Simplify: (a) 16(1+36) (b) 43(263).Simplify: a. 8(258) b. 33(39363).Simplify: (a) (637)(3+47) (b) (x32)(x33).Simplify: (a) (2311)(411) (b) (x3+)(x3+3).Simplify: (537)(3+27)Simplify: (638)(26+8)Simplify: (a) (10+2)2 (b) (1+36)2.Simplify: (a) (65)2 (b) (92 10)2.Simplify: (325)(3+25)Simplify: (4+57)(457).In the following exercises, simplify. 165. a. 8252 b. 5m3+2m3 c. 8m42m4In the following exercises, simplify. 166. a. 7232 b. 7p3+2p3 c. 5x33x3In the following exercises, simplify. 167. a. 35+65 b. 9a3+3a3 c. 52z4+2z4In the following exercises, simplify. 168. a. 45+85 b. m34m3 c. n+3nIn the following exercises, simplify. 169. a. 32a42a+52a b. 53ab433ab423ab4In the following exercises, simplify. 170. a. 11b511b+311b b. 811cd4+511cd4911cd4In the following exercises, simplify. 171. a. 83c+23c93c b. 249q354pq3+44pq3In the following exercises, simplify. 172. a. 35d+85d115d b. 112rs392rs3+32rs3In the following exercises, simplify. 173. a. 2775 b. 4033203 c. 12324+231624In the following exercises, simplify. 174. a. 7298 b. 243+813 c. 12804234054In the following exercises, simplify. 175. a. 48+27 b. 543+1283 c. 654323204In the following exercises, simplify. 176. a. 45+80 b. 8131923 c. 52804+734054In the following exercises, simplify. 177. a. 172a550a5 b. 980p446405p44In the following exercises, simplify. 178. a. 48b575b5 b. 864q633125q63In the following exercises, simplify. 179. a. 180c7120c7 b. 2162r104+432r104180E181E182E183EIn the following exercises, simplify. 184. a. (45)(510) b. (293)(793)In the following exercises, simplify. 185. a. (56)(12) b. (2184)(94)In the following exercises, simplify. 186. a. (27)(214) b. (384)(564)In the following exercises, simplify. 187. a. (412z3)(39z) b. (53x33)(318x33)In the following exercises, simplify. 188. a. (32x3)(718x2) b. (620a23)(216a33)In the following exercises, simplify. 189. a. (27z3)(314z8) b. (28y24)(212y34)In the following exercises, simplify. 190. a. (42k5)(332k6) b. (6b34)(38b34)In the following exercises, multiply. 191. a. 7(5+27) b. 63(4+183)In the following exercises, multiply. 192. a. 11(8+411) b. 33(93+183)In the following exercises, multiply. 193. a. 11(3+411) b. 34(544+184)In the following exercises, multiply. 194. a. 2(5+92) b. 24(124+244)In the following exercises, multiply. 195. (7+3)(93)In the following exercises, multiply. 196. (82)(3+2)In the following exercises, multiply. 197. a. (932)(6+42) b. (x33)(x3+1)In the following exercises, multiply. 198. a. (327)(547) b. (x35)(x33)In the following exercises, multiply. 199. a. (1+310)(5210) b. (2x3+6)(x3+1)In the following exercises, multiply. 200. a. (725)(4+95) b. (3x3+2)(x32)In the following exercises, multiply. 201. (3+10)(3+210)In the following exercises, multiply. 202. (11+5)(11+65)In the following exercises, multiply. 203. (27511)(47+911)In the following exercises, multiply. 204. (46+713)(86313)In the following exercises, multiply. 205. a. (3+5)2 b. (253)2In the following exercises, multiply. 206. a. (4+ 11)2 b. (325)2In the following exercises, multiply. 207. a. (96)2 b. (10+37)2In the following exercises, multiply. 208. a. (5 10)2 b. (8+32)2In the following exercises, multiply. 209. (4+2)(42)In the following exercises, multiply. 210. (7+10)(710)In the following exercises, multiply. 211. (4+93)(493)In the following exercises, multiply. 212. (1+82)(182)In the following exercises, multiply. 213. (1255)(12+55)In the following exercises, multiply. 214. (943)(9+43)In the following exercises, multiply. 215. (3x3+2)(3x32)In the following exercises, multiply. 216. (4x3+3)(4x33)2327+3448175k463k456162+316128243+/81312804234054813441343134512c4327c680a545a5357514482193293864q633125q6311111011321(46)(18)(743)(3183)(412x5)(26x3)( 29)2(417)(317)(4+17)(3+17)(38a24)(12a34)(632)23(433)33(293+183)(6+3)(6+63)Explain the when a radical expression is in simplest form.Explain the process for determining whether two radicals are like or unlike. Make sure your answer makes sense for radicals containing both numbers and variables.Explain why (n)2 is always non-negative, for n0. Explain why (n)2 is always non-positive, for n0.Use the binomial square pattern to simplify (3+2)2. Explain all your steps.Simplify: (a) 50s3128s (b) 56a37a43.Simplify: (a) 75q5108q (b) 72b239b53.Simplify: (a) 162x 10y22x6y6 (b) 128x2y 132x 1y23.Simplify: (a) 300m3n73m5n (b) 81pq 133p 2q53.Simplify: 64x4y52xy3.Simplify: 96a5b42a3b.Simplify: (a) 513 (b) 332 (c) 22x.Simplify: (a) 65 (b) 718 (c) 55x.Simplify: (a) 173 (b) 5123 (c) 59y3.Simplify: (a) 123 (b) 3203 (c) 225n3.Simplify: (a) 134 (b) 3644 (c) 3125x4.Simplify: (a) 154 (b) 71284 (c) 44x4Simplify: 315.Simplify: 246.Simplify: 5x+2.Simplify: 10y3.Simplify: p+2p2.Simplify: q10q+10In the following exercises, simplify. 245. a. 12872 b. 1283543In the following exercises, simplify. 246. a. 4875 b. 813243In the following exercises, simplify. 247. a. 200m598m b. 54y232y53In the following exercises, simplify. 248. a. 108n7243n3 b. 54y316y43In the following exercises, simplify. 249. a. 75r3108r7 b. 24x7381x43In the following exercises, simplify. 250. a. 196q484q5 b. 16m4354m3In the following exercises, simplify. 251. a. 108p5q23p3q6 b. 16a4b232a 2b3In the following exercises, simplify. 252. a. 98rs 102r3s4 b. 375y4z 233y 2z43