实验中学幂的乘方

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,幂的乘方,1,计算,:,2,2,2,3,2,4,(2) 2,2,2,3,2,4,(3)a,2,a,2,a,2,(4)a,m,a,m,a,m,同底数幂相乘的运算法则：,a,m,a,n,a,m,n,（,m,，,n,都是正整数）,2,一个正方体的棱长是,10,它的体积是多少,?,如果它的棱长是,10,2,它的体积又是多少,?,如果是,10,4,呢,?,10,3,=10 1010,(10,2,),3,(10,4,),3,=10,6,=10,12,=10,2,10,2,10,2,=10,4,10,4,10,4,怎样计算,?,3,(1)(3,2,),3,=( )( )( )=3,( ),(2)(a,2,),3,=( )( )( )=a,( ),(3)(a,m,),3,=( )( )( )=a,( ),(m,为正整数）,根据乘方的意义与同底数幂的乘法填空，看看计算的结果有什么规律？,3,2,3,2,3,2,6,6,a,2,a,2,a,2,a,m,a,m,a,m,3m,(3,2,),3,=,3,2,3,=3,6,(a,2,),3,=,a,2,3,=a,6,(a,m,),3,=,a,m,3,=a,3m,对于任意底数,a,与任意正整数,m,、,n,（,4,）（,a,m,),n,=a,m,a,m,a,m,=a,m+m+m,=a,mn,n,个,a,m,n,个,m,4,幂的乘方运算法则,（,a,m,）,n,a,mn,（,m,，,n,都是正整数）,即幂的乘方,底数不变,指数相乘,.,5,例 计算,:,(1)(10,3,),5,(2)(a,4,),2,(3)(a,m,),2,(4)-(,X,4,),3,解,:,(1) (10,3,),5,=10,35,=10,15,(2) (a,4,),2,=a,44,=a,16,(3) (a,m,),2,=a,m2,=a,2m,(4) -(X,4,),3,=-X,43,=-X,12,6,下面计算是否正确？如有错误请改正。,(1)X,3,X,3,=2X,3,(2) X,2,+X,2,=X,4,(3) a,4,a,2,=a,6,(4) (a,3,),7,=a,10,(5,) (X,5,),3,=X,15,(6)-(a,3,),4,=a,12,X,3,X,3,=X,6,X,2,+X,2,=2X,2,(a,3,),7,=a,21,-(a,3,),4,=-a,12,7,例,2,把,化成,的形式,.,解：,8,例 计算,:,(1) (X,2,),m+1,(2)-(X-Y),5,2,(3) (,a,2,),3,(a,4,),3,(4)(X,2,),2,X,4,+(X,2,),4,(1) (X,2,),m+1,=X,2 (m+1),=X,2m+2,(2)-(X-Y),5,2,=(X-Y),52,=(X-Y),10,(3) (a,2,),3,(a,4,),3,=,a,6,a,12,=a,18,(4)(X,2,),2,X,4,+(X,2,),4,=X,4,X,4,+X,8,=X,8,+X,8,=2X,8,解,:,9,例,3,计算：,2,3,4,2,),(,),1,(,a,a,a,+,.,解,:,原式,=,10,练习,:,计算,:,(a,m-3,),2,a,6,(,X,n,),2,-2,X,2n,4X,2,Y(-X,2,),3,Y,11,想一想,：,同底数幂的乘法法则,与,幂的乘方法则,有什么相同点和不同点？,12,这节课你学到了什么？,畅所欲言！,13,幂的乘方法则：,同底数幂的乘法法则：,n,m,n,m,a,a,a,+,=,.,(,其中,m , n,都是,正整数,),注意同底数幂的乘法法则,与幂的乘方的区别,.,14,再见,15,