冪的乘方新建中學(xué)潘巧燕1/20計(jì)算:22×23×24(2)22×23×24(3)a2·a2·a2(4)am·am·am同底數(shù)冪相乘運(yùn)算法則：am·an＝am＋n（m，n都是正整數(shù)）2/20一個(gè)正方體棱長(zhǎng)是10,它體積是多少?假如它棱長(zhǎng)是102,它體積又是多少?假如是104呢?103=10×10×10(102)3(104)3=106=1012=102×102×102=104×104×104怎樣計(jì)算?3/20(1)(32)3=()×()×()=3()(2)(a2)3=()×()×()=a()(3)(am)3=()×()×()=a()(m為正整數(shù)）依據(jù)乘方意義與同底數(shù)冪乘法填空，看看計(jì)算結(jié)果有什么規(guī)律？32323266a2a2a2amamam3m(32)3=32

×3=36(a2)3=a2

×3=a6(am)3=am

×3=a3m對(duì)于任意底數(shù)a與任意正整數(shù)m、n（4）（am)n=am·am…·am=am+m+…+m=amnn個(gè)amn個(gè)m4/20冪乘方運(yùn)算法則（am）n＝amn（m，n都是正整數(shù)）即冪乘方,底數(shù)不變,指數(shù)相乘.5/20例計(jì)算:(1)(103)5(2)(a4)2(3)(am)2(4)-(X4)3解:(1)(103)5=103×5=1015

(2)(a4)2=a4×4=a16(3)(am)2=am×2=a2m(4)-(X4)3=-X4×3=-X126/20下面計(jì)算是否正確？如有錯(cuò)誤請(qǐng)更正。(1)X3·X3=2X3

(2)X2+X2=X4(3)a4·a2=a6

(4)(a3)7=a10(5)(X5)3=X15

(6)-(a3)4=a12√√××××X3·X3=X6X2+X2=2X2(a3)7=a21-(a3)4=-a127/20例2把化成形式.解：8/20例計(jì)算:(1)(X2)m+1(2)[-(X-Y)5]2(3)–(a2)3·(a4)3

(4)(X2)2·X4+(X2)4(1)(X2)m+1=X2(m+1)=X2m+2(2)[-(X-Y)5]2=(X-Y)5×2=(X-Y)10(3)–(a2)3·(a4)3=–a6·a12=–a18(4)(X2)2·X4+(X2)4=X4·X4+X8=X8+X8=2X8解:9/20例3計(jì)算：2342)()1(aaa+.解:原式=10/20練習(xí):計(jì)算:(am-3)2·a6

(Xn)2-2X2n

4X2Y·(-X2)3Y11/20想一想：同底數(shù)冪乘法法則與冪乘方法則有什么相同點(diǎn)和不一樣點(diǎn)？12/2013/2014/2015/2016/20這節(jié)課你學(xué)到了什么？暢所欲言！17/20冪乘方法則：同底數(shù)冪乘法法則：