《幂的乘方与积的乘方》习题精选、典型例题.doc

幂的乘方与积的乘方习题精选、典型例题习题精选选择题：1计算(a3)2+a2a4的结果等于( )A2a9B2a6Ca6+a8Da122下列等式一定成立的有( )x2m = (x2)m； x2m = (xm)2；(xm)2 = x2m； x2m = (x2)mA4个B3个C2个D1个3化简(a5)2+(a2)5的结果为( )A2a7B0C2a10D2a104n为正整数时，3n+281n+3的计算结果为( )A32n+5B33n+5C35n+14D35n+125计算(2a2)2的结果是( )A2a4B2a4C4a4D4a46计算a6(a2b)3等于( )Aa11b13Ba12b3Ca14b3D3a12b7下列运算不正确的是( )A(a5)2 = a10Bb3b = b4C(2a2b)3 = 8a6b3Db5b5 = b258下列计算过程正确的是( )Ax3+x3 = x3+3 = x6 Bx3x3 = x33 = x9Cxx3x5 = x3+5 = x8 Dx2(x)3 = x2+3 = x5解答题：1解方程：9x = 3x+12比较355、444、533的大小3计算：(x)2(x)2n+1x3 (n为正整数)4用简便方法计算：(9)3()3()35计算：2x2y4+(2xy2)23x2(y2)26如果a2n = 5，bn = 3，求：(1)(ab)4n；(2)(a2b3)n答案：选择题：1B 2B 3B 4C 5C 6B 7D 8D解答题：1x = 1；2444355533；3x2n+6；48；53x2y4；6(1)2025；(2)135典型例题1下列计算正确的是( )A(xy)3 = xy3B(2xy)3 = 6x3y3C(3x2)3 = 27x5D(a2b)n = a2nbn答案：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D2下列各式错误的是( )A(23)4 = 212B( 2a)3 = 8a3C(2mn2)4 = 16m4n8D(3ab)2 = 6a2b2答案：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C3下列计算中，错误的是( )Amnm2n+1 = m3n+1B(am1)2 = a2m2C(a2b)n = a2nbnD(3x2)3 = 9x6 答案：D说明：mnm2n+1 = mn+2n+1 = m3n+1，A中计算正确；(am1)2 = a2(m1) = a2m2，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D4计算a6(a2)3的结果等于( )Aa11Ba 12Ca14Da36答案：B说明：a6(a2)3 = a6a23 = a6a6 = a6+6 = a12，所以答案为B5下列各式计算中，正确的是( )A(a3)3 = a6B(a5)4 = a20C(a)53 = a15D(a)23 = a6答案：D说明：(a3)3 = a33 = a9，A错；(a5)4 = a54 = a20，B错；(a)53 = (a)53 = (a)15 = a15，C错；(a)23 = (a)23 = (a)6 = a6，D正确，答案为D6下列各式计算中，错误的是( )A(m6)6 = m36B(a4)m = (a2m)2Cx2n = (xn)2Dx2n = (x2)n答案：D说明：(m6)6 = m66 = m36，A计算正确；(a4)m = a4m，(a2m)2