(必修一同步2.1.1第2课时分数指数幂.ppt

1．初中我们学过平方差、立方差和完全平方公式，它们别为 a2－b2＝__________________ a3－b3＝__________________ a3＋b3＝__________________ (a＋b)2＝__________________ (a－b)2＝__________________ 2．有理数指数幂的运算性质 (1)aras＝________(a＞0，r，s∈Q)； (2)(ar)s＝________(a＞0，r，s，∈Q)； (3)(ab)r＝________(a＞0，b＞0，r∈Q)． [归纳总结]　三条运算性质的文字叙述： (1)同底数幂相乘，底数不变，指数相加； (2)幂的乘方，底数不变，指数相乘； (3)积的乘方等于乘方的积． 3．无理数指数幂 一般地，无理数指数幂aα(a＞0，α是无理数)是一个确定的________．有理数指数幂的运算性质同样适用于无理数指数幂． [知识拓展]　在引入分数指数幂的概念后，指数概念就实现了由整数指数幂向有理数指数幂的扩展；在引入无理数指数幂的概念后，指数概念就实现了由有理数指数幂向实数指数幂的扩展． 探究1.关键是理解分数指数幂的意义，先将根式化为分数指数幂的形式． 探究2.运用分数指数幂的运算性质进行化简． [规律总结]　1.幂的运算的常规方法 (1)化负指数幂为正指数幂； (2)化根式为分数指数幂； (3)化小数为分数进行运算． 2．分数指数幂及根式化简结果的具体要求 利用分数指数幂进行根式计算时，结果可化为根式形式或保留分数指数幂的形式，不强求统一用什么形式，但结果不能既有根式又有分数指数幂，也不能同时含有分母和负指数． (2)解决此类问题的一般步骤是 4．下列各式运算错误的是(　　) A．(－a2b)2(－ab2)3＝－a7b8 B．(－a2b3)3÷(－ab2)3＝a3b3 C．(－a3)2(－b2)3＝a6b6 D．[(a3)2(－b2)3]3＝－a18b18 [答案]　C Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 易错点一　利用有理数指数幂的运算性质进行运算时，忽略了底数需大于0 ●误区警示 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 易错点二　利用有理数指数幂的运算性质进行运算时，忽略了底数需相同 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. 当 堂 检 测 Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created with Aspose.Slides for .NET 3.5 Client Profile 5.2.0.0. Copyright 2004-2011 Aspose Pty Ltd. Evaluation only. Created