江苏省无锡市七级数学下册 8.2《幂的乘方》课件 苏科版.ppt

初中数学七年级下册(苏科版) 幂的乘方 幂的乘方 1回顾与思考??回顾回顾& & 思考思考? a a m m· · a a n n( (a a· ·a a· · ……· ·a a) ) n n 个个a a= =( (a a· ·a a· · ……· ·a a) ) m m 个个a a= = a a· ·a a· · ……· ·a a ( (m m+ +n n) ) 个个a a = = a a m m+ +n n ??幂的意义幂的意义: :a a· ·a a· · ……· ·a a n n 个个a aa a n n= = 同底数幂乘法的运算性质: 同底数幂乘法的运算性质: a a m m· · a a n n= = ??a a m m+ +n n( (m m, ,n n都是正整数都是正整数) ) 推导推导过程过程 2做一做做一做做一做计算下列各式,并说明理由计算下列各式,并说明理由. . (1) (1) (6 (6 2 2) ) 4 4; ; (2) (2) (a (a 2 2) ) 3 3; ; (3) (3) (a (a m m) ) 2 2 ; ; (4) (4) (a (a m m) ) n n. . 解: 解: (1) (1) (6 (6 2 2) ) 4 4 (2) (2) (a (a 2 2) ) 3 3 (3) (3) (a (a m m) ) 2 2 = 6 = 6 2 2· ·6 6 2 2· ·6 6 2 2· ·6 6 2 2 =6 =6 2+2+2+2 2+2+2+2 =6 =6 8 8 = a = a 2 2· ·a a 2 2· ·a a 2 2 =a =a 2+2+2 2+2+2 =a =a 6 6 =a =a m m· ·a a m m =a =a m+m m+m (4) (4) ( (a a m m) ) n n= =a a m m· ·a a m m· · ……· ·a a m m个个a a m m =a =a m+m+ m+m+ ……+m +m =a =a mn mn ( (幂的意义) 幂的意义) ( (同底数幂的乘法性质) 同底数幂的乘法性质) ( (乘法的意义) 乘法的意义) 猜想猜想= = =6 =6 2 2 × × 4 4 ; ; (6 (6 2 2) ) 4 4 =a =a 2 2 × × 3 3 ; ; (a (a 2 2) ) 3 3 =a =a 2m 2m ; ; (a (a m m) ) 2 2a a mn mn 证证明明 n n个个m m n n 3 (a (a m m) ) n n =a =a mn mn (m,n (m,n 都是正整数都是正整数) )底数底数, , 指数指数. . 幂的乘方, 幂的乘方, 幂的乘方法则不变不变相乘相乘 4 【例1】计算: ⑴(10 4) 2 ; ⑵ (a m) 4 ( m为正整数); ⑶-(x 3) 2 ; ⑷(-y n) 5 ; ⑸ [( x-y ) 2] 3 ; ⑹ [(a 3) 2] 5.⑹[(a 3) 2] 5= = =10 10 4 4 × ×2 2= =10 10 8 8 ; ;⑴⑴ (10 (10 4 4) ) 2 2解: 解: ⑵⑵(a m) 4=a m ×4=a 4m ; ; ⑶⑶-(x 3) 2=- x 3 ×2=- x 6 ; ; ⑷(-y n) 5=-y n ×5=-y 5n; ; ⑸ [(x-y) 2] 3 =(x-y) 2×3=(x-y) 6; ; (a m) n=a mn(m,n都是正整数) 幂的乘方,底数不变,指数相乘(a 3×2) 5=a 3×2×5=a 30. 推广: [(a m) n] p=(a mn) p =a mnp (m、n、p都是正整数). =- (y n) 5 5 随堂练****1、计算: na xx a 23 243 52 33) )(4( ) )(3( )()2( )10 )(1(???(5)(a m) 4(6)(x 4) 3·(x 2) 8(7)(a 2) 3·(a 3) 4(8)(a m+3) 2(9)[(x-3y) m] 3(10)9 m·27 n 注注1 1:幂的底数和指数不仅仅是单独字母:幂的底数和指数不仅仅是单独字母或数字,也可以是某个单项式和多项式或数字,也可以是某个单项式和多项式. . 6 【例2】计算: ⑴x 2·x 4+(x 3) 2;⑵(a 3) 3·(a 4) 3解: ⑴原式=x 2+4+x 3×2=x 6+x 6=2x 6⑵原式= a 9·a 12=a 9+12 =a 21 ---①幂的乘方-