15.2.3 积的乘方积的乘方探究填空,看看运算过程用到哪些运算律?运算结果有什么规律?(1) (ab)2=(ab) (ab)=(aa) (bb)=a( )b ( );(2) (ab)3= _ = _ =a ( )b( ).对于任意底数对于任意底数a,b与任意正整数与任意正整数n,(ab)n= (ab)(ab)(ab) = a a a b b b = a n b n. n个个abn个个an个个b一般地一般地,我们有我们有(ab)n=anbn(n为正整数为正整数)即即积的乘方积的乘方,等于把积的每一个因等于把积的每一个因式分别乘方式分别乘方,再把所得的幂相乘再把所得的幂相乘.例例3 计算计算: (1) (2a)3 ; (2) (-5b)3 ; (3) (xy2)2 ; (4) (-2x3)4.解解: (1) (2a)3=23a3 = 8a3； (2) (-5b)3=(-5)3b3=-125b3； (3) (xy2)2=x2(y2)2=x2y4； (4) (-2x3)4=(-2)4(x3)4=16x12.练习练习计算计算: (1) (ab)4 ; (2) (-2xy)3; (3) (-3102)3 ; (4) (2ab2)3.(1) a4b4 ; (2) 8x3y3;(3) 2.7107; (4) 8a3b6.已知已知,xm= ,xn=3.求下列各式的值求下列各式的值:(1)x m+n; (2) x2mx2n; (3) x 3m+2n.解解: (1) x m+n=x mx n= 3= ; (2) x2mx2n=(x m )2(x n)2=( )232= 9 = ; (3) x 3m+2n=x3mx2n=(x m)3(x n)2=( )332 = 9 =