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【330017】15.2.3整数指数幂(1)

时间:2025-02-07 09:17:59 作者: 字数:2551字

 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

15.2.3整数指数幂(1

学习目标

1、知道负整数指数幂 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> a≠0n是正整数).

2、掌握负整数指数幂的运算性质.

学习重点:掌握整数指数幂的运算性质.

学习难点:灵活运用负整数指数幂的运算性质

课前预习

1、正整数指数幂的运算性质是什么?

1)同底数的幂的乘法:

2)幂的乘方:

3)积的乘方:

4)同底数的幂的除法:

5)商的乘方:

60指数幂,即当a≠0时, <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> .

2、探索新知:

 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 中,当 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 时,产生0次幂,即当a≠0时, <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 。那么当 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 时,会出现怎样的情况呢?如计算: <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 由此得出: <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

a≠0时, <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 由此得到  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> a≠0)。

因此规定负整数指数幂的运算性质:当n是正整数时, <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> a≠0.

1纳米=10-9米,即1纳米= <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

填空:  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> = , 若 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =12,则 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =

计算: <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> =

二、学教互动:(1)将 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的结果写成只含有正整数指数幂的形式 (分析:应用推广后的整数指数幂的运算性质进行计算,与用正整数指数幂的运算性质进行计算一样,但计算结果有负指数幂时,要写成分式形式).




2)用小数表示下列各数

 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 2 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>






课内探究

选择:1、若 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

A <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> B <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

C <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> D <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

2、。已知 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> ,则 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>  <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的大小关系是( )

A <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> B <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

C <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> D <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

3、计算:(1 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>2 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>



当堂检测

1、已知 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 有意义,求 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的取值范围。



2(山东淄博)化简 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的结果是(  )

A <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> Ba C <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> D <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

3、化简: <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 等于(  )

A <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> Bxy4z2

Cxy4z4 Dy5z

课后训练

1、计算 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>(  )

A <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> B <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

C、-2 D2

2、化简 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> ÷ <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的结果是(  )

Aa1 B <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a>

C <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> Da1

3、若m等于它自身的倒数,则分式 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> ÷ <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的值为__________

4、化简 <a href="/tags/191/" title="整数" class="c1" target="_blank">整数</a> <a href="/tags/902/" title="指数" class="c1" target="_blank">指数</a> 的结果是______


5、计算

(1) (3×10-8)×(4×103)







(2) (2×10-3)2÷(10-3)3