【概念学习】现规定:求若干个相同且都不等于0的有理数的商的运算叫做除方,例如:
,
类比有理数的乘方,我们把
, 写作:
, 读作“2的圈4次方”,
, 写作:
, 读作“(-3)的圈3次方”,一般地把
, 写作:
, 读作“a的圈n次方”.
【初步探究】
(1)直接写出计算结果:
_________;
_________.
【深入思考】
我们知道,有理数的减法运算可以转化为加法运算,除法运算可以转化为乘法运算,那么有理数的除方运算如何转化为乘方运算呢?
![](http://tikupic.21cnjy.com/ct20241o/ea/6c/ea6c04a61088c18cb08350105d8a7846.png)
(2)试一试:仿照上面的算式,把下列除方运算直接写成幂的形式:
①
__________________;
②
__________________.
(3)算一算:![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmsup%3E%3Cmrow%3E%3Cmn%3E12%3C%2Fmn%3E%3C%2Fmrow%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3Cmo%3E%C3%B7%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced+open%3D%22%28%22+close%3D%22%29%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E4%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmi+mathvariant%3D%22normal%22%3E%E2%91%A2%3C%2Fmi%3E%3C%2Fmsup%3E%3Cmo%3E%C3%97%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced+open%3D%22%28%22+close%3D%22%29%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmi+mathvariant%3D%22normal%22%3E%E2%91%A3%3C%2Fmi%3E%3C%2Fmsup%3E%3Cmo%3E%2B%3C%2Fmo%3E%3Cmsup%3E%3Cmrow%3E%3Cmfenced+open%3D%22%28%22+close%3D%22%29%22%3E%3Cmrow%3E%3Cmo%3E%E2%88%92%3C%2Fmo%3E%3Cmfrac%3E%3Cmn%3E1%3C%2Fmn%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmfenced%3E%3C%2Fmrow%3E%3Cmi+mathvariant%3D%22normal%22%3E%E2%91%A4%3C%2Fmi%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3C%2Fmath%3E)