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1、9.99.9積的乘方積的乘方知識(shí)回顧知識(shí)回顧填空：填空：1.a1.amm+a+amm=_,=_,依據(jù)依據(jù)_._.2.a2.a3 3aa5 5=_ ,=_ ,依據(jù)依據(jù)_3.3.若若a amm=8,a=8,an n=30,=30,則則a am+nm+n=_.=_.依據(jù)依據(jù)_4.(a4.(a4 4)3 3=_,=_,依據(jù)依據(jù)_5.(m5.(m4 4)2 2+m+m5 5mm3 3=_,(a=_,(a3 3)5 5(a(a2 2)2 2=_.=_.2a2amm合并同類項(xiàng)法則合并同類項(xiàng)法則a a8 8同底數(shù)冪的乘法同底數(shù)冪的乘法240240a a1212冪的乘方冪的乘方2m2m8 8a a1919逆用同
2、底數(shù)冪的乘法逆用同底數(shù)冪的乘法2公開課(1(12)2)4 4_;1_;14 42 24 4 =_;=_;3 3(-2)(-2)3 3_;3_;33 3(-2)(-2)3 3=_;=_;()()2 2 ;=;=1111232316161616216216216216你發(fā)現(xiàn)了什么你發(fā)現(xiàn)了什么?2222()()1111(2323136136填空：填空：3公開課(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))猜想猜想:你能說(shuō)明理由嗎？你能說(shuō)明理由嗎？=(ab)=(ab)(ab)(ab)(ab)(ab)n n個(gè)個(gè)abab =(a =(aa aa)a)(b(bb bb)b)n n個(gè)個(gè)a na
3、n個(gè)個(gè)b b =a =an nb bn n(ab)(ab)n n(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n結(jié)論：結(jié)論：結(jié)論：結(jié)論：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))你能說(shuō)明理由嗎？你能說(shuō)明理由嗎？=(ab)=(ab)(ab)(ab)(ab)(ab)n n個(gè)個(gè)abab =(a =(aa aa)a)(b(bb bb)b)n n個(gè)個(gè)a na n個(gè)個(gè)b b =a =an nb bn n(ab)(ab)n n冪的意義冪的意義乘法的交換乘法的交換律、結(jié)合律律、結(jié)合律乘方的意義乘方的意義(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正
4、整數(shù))a an nb bn n積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：結(jié)論：結(jié)論：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n你能用文字語(yǔ)言敘述這個(gè)性質(zhì)嗎？你能用文字語(yǔ)言敘述這個(gè)性質(zhì)嗎？積的乘方積的乘方,把積的每一個(gè)因式分別乘方把積的每一個(gè)因式分別乘方,再把所得的冪相乘再把所得的冪相乘.積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n 積的乘方積的乘方,把積的每
5、一個(gè)因式分別乘方把積的每一個(gè)因式分別乘方,再把所得的冪相乘再把所得的冪相乘.例例1 1 計(jì)算：計(jì)算：(1)(1)（3a)3a)4 4 (2)(-2mx)(2)(-2mx)3 3(3)(-xy(3)(-xy2 2)3 3 (4)()(4)()2 2232xy1.1.計(jì)算：計(jì)算：(1)(1)(-ab)(-ab)5 5 (2)(x (2)(x2 2y y3 3)4 4(3)(2a(3)(2a3 3)2 2 (4)(-3a (4)(-3a3 3)3 32.2.下面的計(jì)算是否正確？如果有錯(cuò)誤，請(qǐng)下面的計(jì)算是否正確？如果有錯(cuò)誤，請(qǐng)改正改正.(1)(1)(xy(xy2 2)3 3=x y=x y6 6(2)
6、(2)(-2b(-2b2 2)2 2=-4b=-4b4 4積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n請(qǐng)你推廣請(qǐng)你推廣:(abc)(abc)n n=a an nb bn nc cn n(n(n為正整數(shù)為正整數(shù))(abc)(abc)n n=(ab)(ab)ccn n=a=an
7、nb bn nc cn n=(ab)(ab)n nc cn n1 1積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n(abc)(abc)n n=a an nb bn nc cn n(n(n為正整數(shù)為正整數(shù))請(qǐng)你推廣請(qǐng)你推廣:(abc)(abc)n n=(ab)(ab)ccn n=a=an nb bn nc cn n=(ab)(ab)n nc cn n積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(a
8、b)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n1 1(abc)(abc)n n=a an nb bn nc cn n(n(n為正整數(shù)為正整數(shù))積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n1 1(abc)(abc)n n=a an nb bn nc cn n(n(n為正整數(shù)為正整數(shù))例例2 2 計(jì)算：計(jì)算：(1)(1)（3xy3xy2 2)2 2(2)(-2ab(2)(-2ab3 3c c2 2)4 4例例3.3.計(jì)算：計(jì)算：(-a
9、)(-a)3.3.(-a)(-a)4 4 3(x 3(x2 2y y2 2)-2(x)-2(x3 3y y3 3)2 2 (3a (3a3 3)2 2+(2a+(2a2 2)3 3 14公開課拓展訓(xùn)練拓展訓(xùn)練 的值求已知?jiǎng)t則若則）若（m，xy，yxx，x，mnnmxbax327216286432222259639440313281（5）若n是正整數(shù)，且 ，求 的值。5,6nnyxnxy2你會(huì)計(jì)算你會(huì)計(jì)算 嗎？嗎？441()22逆用積的乘方逆用積的乘方的運(yùn)算性質(zhì)的運(yùn)算性質(zhì)積的乘方的運(yùn)算性質(zhì)：積的乘方的運(yùn)算性質(zhì)：(ab)(ab)n n=_.(n=_.(n為正整數(shù)為正整數(shù))(ab)(ab)n n=_
10、.(n=_.(n為正整數(shù)為正整數(shù))a an nb bn n1001001()22111222222()().()()().()6122()()=1=1111222222(.)(.)(.)(.)6 6個(gè)個(gè)126 6個(gè)個(gè)2 2解：原式解：原式解：原式解：原式66122()你會(huì)計(jì)算你會(huì)計(jì)算 嗎？嗎？4520 254.441144.().()4101424.().()計(jì)算計(jì)算:.()200820091333 410124()()4 逆用同底數(shù)冪的逆用同底數(shù)冪的乘法運(yùn)算性質(zhì)乘法運(yùn)算性質(zhì)逆用積的乘方逆用積的乘方的運(yùn)算性質(zhì)的運(yùn)算性質(zhì)45144()()441444()41444()()414 逆用冪的乘方逆用冪的乘方的運(yùn)算性質(zhì)的運(yùn)算性質(zhì)42 5124()()()()解：原式解：原式410124()()810122()()4 逆用同底數(shù)冪的逆用同底數(shù)冪的乘法運(yùn)算性質(zhì)乘法運(yùn)算性質(zhì)逆用積的乘方逆用積的乘方的運(yùn)算性質(zhì)的運(yùn)算性質(zhì)8821222()()821222()()逆用冪的乘方逆用冪的乘方的運(yùn)算性質(zhì)的運(yùn)算性質(zhì)冪的乘方的運(yùn)冪的乘方的運(yùn)算性質(zhì)算性質(zhì)2 410122()()解：原式解：原式
9.9 積的乘方【上課材料】
