幂的运算测试题
一、选择题：
1．下列计算中,错误的是( )
A．mn·m2n+1 = m3n+1 B．(−am−1)2 = a 2m−2
C．(a2b)n= a2nbn D．(−3x2)3 = −9x6
2．若xa= 3,xb = 5,则xa+b的值为( )
A．8 B．15
C．35 D．53
3．计算(c2)n•(cn+1)2等于( )
A．c4n+2 B．c
C．c
D．c3n+4
4．与[(− 2a2)3]5的值相等的是( )
A．− 25a30
B． 215a 30
C．(− 2a2)15
D．( 2a)30
5．下列计算正确的是( )
A．(xy)3
= xy3
B．(2xy)3 = 6x3y3
C．(−3x2)3
= 27x5 D．(a2b)n
= a2nbn
6．下列各式错误的是( )
A．(23)4
= 212
B．(− 2a)3 = − 8a3
C．(2mn2)4= 16m4n8 D．(3ab)2 = 6a2b2
7．下列各式计算中,错误的是( )
A．(m6)6
= m36
B．(a4)m = (a 2m)2
C．x2n =
(−xn)2
D．x2n = (−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)2]4
4．如果am= −5,an = 7,求a 2m+n的值．
幂的运算测试题答案：
一、选择题：
1、D
说明：mn·m2n+1 = mn+2n+1
= m3n+1,A中计算正确；(−am−1)2 = a2(m−1) = a 2m−2,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D．
2、B
说明：因为xa = 3,xb = 5,所以xa+b = xa•xb = 3•5 = 15,答案为B．
3、A
说明：(c2)n•(cn+1)2
= c2×n•c2(n+1)
= c2n•c2n+2 = c2n+2n+2
= c4n+2,所以答案为A．
4、C
说明：[(− 2a2)3]5 = (− 2a2)3×5 = (− 2a2)15,所以答案为C．
5、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D．
6、C
说明：(23)4 = 23×4 = 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C．
7、D
说明：(m6)6 = m6×6 = 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：
由32n+1+32n
= 324得3•32n+32n
= 324,
即4•32n = 324,32n = 81 = 34,
∴2n = 4,n = 2
2．解析：因为 2m = 3,4n= 2,8k = 5
所以 8m+2n+k = 8m•82n•8k = (23)m•(82)n•8k
= 23m•(43)n•8k =( 2m)3•(4n)3•8k
= 33•23•5
= 27•8•5
= 1080．
3．答案：x32
[−x2(x3)2]4 = (−x2•x3×2)4
= (−x2•x6)4= (−x2+6)4
= (−x8)4 = x8×4
= x32．
4．答案：a 2m+n = 175
因为am = −5,an = 7,所以a 2m+n = a 2m•an = (am)2•an
= (−5)2•7 = 25•7 =
175