【概念学习】
现规定:求若干个相同的有理数(均不等于0)的商的运算叫做除方,比如
,
等,类比有理数的乘方,我们把
写作
,读作“2的圈3次方”,
写作
,读作“
的圈4次方”,一般地把![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71962aab5422ea115c713ea49c87195.png)
写作
,读作“
的圈
次方”.
(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?
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/ad2a5927-3b4b-40a0-b958-cfc298ad7921.png?resizew=360)
(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:
______,
______.
(3)算一算:
现规定:求若干个相同的有理数(均不等于0)的商的运算叫做除方,比如
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbfa18465de74e7a3a414704f38ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbada1b68a9ef62fa4375799eb9bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbfa18465de74e7a3a414704f38ba39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821158f8fe161c407b0e6f92d1ec95d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cbada1b68a9ef62fa4375799eb9bfb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df1191c76b35c12934a6ba5bf43575c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffa4e8a5782902468171a74d9291228.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b71962aab5422ea115c713ea49c87195.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f5bb89c3ad435f1ef59307b174105ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1a74cb7072e390822418121f1116565.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
(1)直接写出计算结果:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a437757c75071ec7c742e6bba8c60979.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e47c0cd64e78b897e4aa1a78dda7e9.png)
【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?
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/5/ad2a5927-3b4b-40a0-b958-cfc298ad7921.png?resizew=360)
(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:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/965e56207cae5f6f8217183476a4832c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/198de55f1c5471ea83fdc2e1fd6601d9.png)
(3)算一算:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9621cfe34a99b197d38bdbf88282c1b8.png)
21-22七年级·全国·假期作业 查看更多[6]
(已下线)【暑期衔接】专题12《有理数的混合运算》知识讲练-2022年暑假小升初数学衔接(北师大版)(已下线)1.5.1乘方(练习)-2022-2023学年七年级数学上册同步精品课堂(人教版)(已下线)第一章有理数(B卷-拔高卷)-【单元测试】2022-2023学年七年级数学分层训练AB卷【冀教版】广西壮族自治区来宾市武宣县实验初级中学2022-2023学年七年级上学期第一次阶段训练数学试题江苏省无锡市江阴市南闸实验学校2023-2024学年七年级上学期10月月考数学试题2024年安徽省蚌埠市蚌山区中考一模数学试题
更新时间:2023-02-05 09:16:06
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【推荐1】同学们都知道,
表示5与
之差的绝对值,实际上也可理解为5与
两数在数轴上所对的两点之间的距离试探索:
(1)求
______;
(2)同样道理
表示数轴上有理数x所对点到
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(3)类似的
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和
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(4)由以上探索猜想对于任何有理数x,
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdc384304c6cb1023b738ad27886863a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c8889b5af070a720f47f0772d7ae09.png)
(2)同样道理
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/254f3a1a83d0ecd7d8f72bf917873407.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cd806d91b3771e2b71f4ac913a11bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ec0618ae3a4fde6d6220010af229b9a.png)
(3)类似的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57515ae1c55157aa323075b73f727a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01317332a203c898536b1d0459f51d23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059003eb86ae3d2b0aa67372e5733411.png)
(4)由以上探索猜想对于任何有理数x,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3234061743e2fbc7f891cf85e936ee79.png)
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解答题-计算题
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【推荐2】已知有理数a,b,c在数轴上的位如图所示,其中
.
(1)
_______,
________;
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/421a473589d5abdd504fdb110828611a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/24/6657235e-9591-4986-bcc6-ac089025c318.jpg?resizew=189)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892560dcff6af9f66a3f735652f69dd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1817297374e431a1d9087dcc2991d3a9.png)
(2)化简
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/770bf1dc0013a43f4af6dc2cfe54d279.png)
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解答题-计算题
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名校
【推荐1】观察下面的点阵图和相应的等式,探究其中的规律:
![](https://img.xkw.com/dksih/QBM/2023/10/10/3343126606503936/3343189268611072/STEM/c8f3e5e2ec954b78a4fa9a223bc21b92.png?resizew=473)
(1)在④后面的横线上写出相应的等式;
①
;②
;③
;④ ;
(2)请猜想
;
(3)试用含有n 的式子表示这一规律:
;(n为正整数)
(4)请用上述规律计算:
①![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7447f89f1bfcc3163b1bbeaa73e62fdc.png)
②
![](https://img.xkw.com/dksih/QBM/2023/10/10/3343126606503936/3343189268611072/STEM/c8f3e5e2ec954b78a4fa9a223bc21b92.png?resizew=473)
(1)在④后面的横线上写出相应的等式;
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1db1c8f88c5de20586db0cde44d3e28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194969148c9c1b7df23d1c65f16767da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90c94bed97397edf43702cba40b6aec6.png)
(2)请猜想
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310b8412716e848f2465777dfe7423f0.png)
(3)试用含有n 的式子表示这一规律:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92235f4fa95c2466b0c17d770aeb2167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d66e386ee6279aae2f650d0fa40e6b8.png)
(4)请用上述规律计算:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7447f89f1bfcc3163b1bbeaa73e62fdc.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0425c975c69ab276c9b1314986b106f0.png)
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