当前位置:首页 > 七年级 > 数学试卷

【350051】湘教版七年级数学下册课后作业:2.1.1同底数幂的乘法(含答案)

时间:2025-03-06 06:41:09 作者: 字数:2811字
简介:

课时作业(八)

同底数幂的乘法

(30分钟 50)

一、选择题(每小题4,12)

1.计算(-x)2·x3的结果是(  )

A.x5    B.-x5    C.x6    D.-x6

2.下列各式计算正确的个数是(  )

x4·x2=x8;②x3·x3=2x6 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> ;③a5+a7 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> =a12;

(-a)2·(-a2)=-a4;⑤a4·a3=a7.

A.1 B.2 C.3 D.4

3.下列各式能用同底数幂乘法法则进行计算的是(  )

A.(x+y)2·(x-y)2 B.(x+y)2(-x-y)

C.(x+y)2+2 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> (x+y)2 D.(x-y)2(-x-y)

二、填空题(每小题4,12)

4.(2013·天津中考)计算a·a6的结果等于    .

5.2n-2×24=64,n=     <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> .

6.已知2x·2x·8=213,x=    .

三、解答题(26)

7.(8)计算:(1)(- <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 3) <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 3·(-3)4·(-3).

(2)a3·a2-a·(-a)2·a2.

(3)(2m-n)4·(n-2m)3·(2m-n)6.

(4)y·yn+ <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 1-2yn·y2.

8.(8)已知ax=5,ay=4,求下列各式的值:

(1)ax+2. (2)ax+y+1.

【拓展延伸】

9.(10)已知2a=3,2b=6, <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 2c=12,试确定a,b,c之间的关系.

 

 

答案解析

1.【解析】A.(-x)2·x3=x2·x3=x2+3=x5.

2.【解析】B.x4·x2=x4+2=x6,故①错误;x3·x3=x3+3=x6,故②错误;a5a7不是同类项,不能合并,故③错误;(-a)2·(- <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> a2)=a2·(-a2)=-a2·a2=-a2+2=-a4,故④正确;a4·a3=a4+3=a7,故⑤正确.

3.【解 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 析】B.A,D选项底数不相同,不是同底数幂的乘法,C选项不是乘法;(x+y)2(-x-y)=-(x+y)2(x+y)=-(x+y)3.

4.【解析】根据同底数幂的乘法法 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 则“同底数幂相乘,底数不变,指数相加”,所以a·a <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 6=a1+6=a7.

答案:a7

5.【解析】因为 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> 2n-2×24=2n-2+4=2n+2,64=26,

所以2n+2=26,n+2=6,解得n=4.

答案:4

6.【解析】因为2x·2x·8=2x·2x·23=2x+x+3 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> ,

所以x+x+3=13,解得x=5.

答案:5

7.【解析】(1)(-3)3·(-3)4·(-3)=(-3)3+4+1=(-3)8=38.

(2)a3·a2-a·(-a)2·a2=a3+2-a·a2·a2

=a5-a5=0.

(3)(2m-n)4·(n-2m)3·(2m-n)6

=(n-2m)4·(n-2m)3·(n-2m)6

=(n-2m)4+3+6=(n-2m)13.

(4)y·yn+1-2yn·y2=yn+1+1-2yn+2

=yn+2-2yn+2=(1-2)yn+2

=-yn+2.

8.【解析】(1)ax+2=ax×a2=5a2.

(2)ax+y+1=ax·ay·a=5×4×a=20a.

9.【解析】方法一:因为12 <a href="/tags/46/" title="答案" class="c1" target="_blank">答案</a> <a href="/tags/55/" title="数学" class="c1" target="_blank">数学</a> <a href="/tags/195/" title="乘法" class="c1" target="_blank">乘法</a> <a href="/tags/381/" title="作业" class="c1" target="_blank">作业</a> =3×22=6×2,

所以2c=12=3×22=2a×22=2a+2,

c=a+2,①

又因为2c=12=6×2=2b×2=2b+1,

所以c=b+1,②

+②2c=a+b+3.

方法二:因为2b=6=3×2=2a×2=2a+1,

所以b=a+1,①

又因为2c=12=6×2=2b×2=2b+1,

所以c=b+1,②

-②2b=a+c.

www.ishijuan.cn 爱试卷为中小学老师学生提供免费的试卷下载关注”试卷家“微信公众号免费下载试卷