14．1幂的运算习题精选.doc

习题精选一、选择题：1下列计算中，错误的是( )Amnm2n+1 = m3n+1 B(am1)2 = a 2m2C(a2b)n = a2nbnD(3x2)3 = 9x6 2若xa = 3，xb = 5，则xa+b的值为( )A8 B15C35 D533计算(c2)n(cn+1)2等于( )Ac4n+2Bc Cc Dc3n+44与( 2a2)35的值相等的是( )A 25a30 B 215a 30 C( 2a2)15 D( 2a)305下列计算正确的是( )A(xy)3 = xy3 B(2xy)3 = 6x3y3C(3x2)3 = 27x5D(a2b)n = a2nbn6下列各式错误的是( )A(23)4 = 212 B( 2a)3 = 8a3C(2mn2)4 = 16m4n8 D(3ab)2 = 6a2b27下列各式计算中，错误的是( )A(m6)6 = m36 B(a4)m = (a 2m)2Cx2n = (xn)2 Dx2n = (x2)n二、解答题：1已知32n+1+32n = 324，试求n的值2已知 2m = 3，4n = 2，8k = 5，求 8m+2n+k的值3计算：x2(x3)24 4如果am = 5，an = 7，求a 2m+n的值答案：一、选择题：1、D 说明：mnm2n+1 = mn+2n+1 = m3n+1，A中计算正确；(am1)2 = a2(m1) = a 2m2，B中计算正确； (a2b)n = (a2)nbn = a2nbn，C中计算正确；(3x2)3 = (3)3(x2)3 = 27x6，D中计算错误；所以答案为D2、B 说明：因为xa = 3，xb = 5，所以xa+b = xaxb = 35 = 15，答案为B3、A 说明：(c2)n(cn+1)2 = c2nc2(n+1) = c2nc2n+2 = c2n+2n+2 = c4n+2，所以答案为A4、C 说明：( 2a2)35 = ( 2a2)35 = ( 2a2)15，所以答案为C5、D 说明：(xy)3 = x3y3，A错；(2xy)3 = 23x3y3 = 8x3y3，B错；(3x2)3 = (3)3(x2)3 = 27x6，C错；(a2b)n = (a2)nbn = a2nbn，D正确，答案为D6、C 说明：(23)4 = 234 = 212，A中式子正确；( 2a)3 = (2) 3a3 = 8a3，B中式子正确；(3ab)2 = 32a2b2 = 9a2b2，C中式子错误；(2mn2)4 = 24m4(n2)4 = 16m4n8，D中式子正确，所以答案为C7、D 说明：(m6)6 = m66 = m36，A计算正确；(a4)m = a 4m，(a 2m)2 = a 4m，B计算正确；(xn)2 = x2n，C计算正确；当n为偶数时，(x2)n = (x2)n = x2n；当n为奇数时，(x2)n = x2n，所以D不正确，答案为D二、解答题：1解：由32n+1+32n = 324得332n+32n = 324，即432n = 324，32n = 81 = 34，2n = 4，n = 22解析：因为 2m = 3，4n = 2，8k = 5所以 8m+2n+k = 8m82n8k = (23)m(82)n8k = 23m(43)n8k = ( 2m)3(4n)38k = 33235 = 2785 = 10803答案：x32解：x2(x3)24 = (x2x32)4 = (x2x6)4 = (x2+6)4 = (x8)4 = x84 = x324答案