《单项式除以单项式》典型例题
例1 计算：
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=128&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"128","h":"41","dataType":"gif","c":"word/media/image1.png"})
； （2）；
（3）![](https://wkrtcs.bdimg.com/rtcs/image?w=133&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"133","h":"25","dataType":"gif","c":"word/media/image3.png"})
．
例2 计算：
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=172&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"172","h":"49","dataType":"gif","c":"word/media/image4.png"})
； （2）．
例3 计算：
（1）![](https://wkrtcs.bdimg.com/rtcs/image?w=246&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"246","h":"25","dataType":"gif","c":"word/media/image6.png"})
；
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=240&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"240","h":"28","dataType":"gif","c":"word/media/image7.png"})
．
参考答案
例1 分析 ：（1）题根据法则分三部分求商的因式：①![](https://wkrtcs.bdimg.com/rtcs/image?w=99&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"99","h":"45","dataType":"gif","c":"word/media/image8.png"})
作为商的系数；②，，同底数相除，作为商的因式；③，只在被除式里含有的字母，则连同它的指数作为商的一个因式．（2）题应先算乘方，再算除法．（3）题应用作为整体进行运算．
解：（1）
![](https://wkrtcs.bdimg.com/rtcs/image?w=221&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"221","h":"45","dataType":"gif","c":"word/media/image13.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=147&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"147","h":"45","dataType":"gif","c":"word/media/image2.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=137&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"137","h":"45","dataType":"gif","c":"word/media/image15.png"})
（3）![](https://wkrtcs.bdimg.com/rtcs/image?w=133&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"133","h":"25","dataType":"gif","c":"word/media/image18.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=185&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"185","h":"33","dataType":"gif","c":"word/media/image19.png"})
说明：在运算结果中要注意不多不漏，如（1）题![](https://wkrtcs.bdimg.com/rtcs/image?w=104&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"104","h":"24","dataType":"gif","c":"word/media/image10.png"})
，商式里不能多出字母，被除式里不能漏掉．
例2 分析：此题是乘方、乘除混合运算，要注意运算顺序，有乘方有要先算乘方．
解：（1）
![](https://wkrtcs.bdimg.com/rtcs/image?w=116&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"116","h":"45","dataType":"gif","c":"word/media/image22.png"})
（2）![](https://wkrtcs.bdimg.com/rtcs/image?w=201&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"201","h":"49","dataType":"gif","c":"word/media/image5.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=221&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"221","h":"45","dataType":"gif","c":"word/media/image24.png"})
说明:（1）计算时一定要看清运算符号，正确计算．（2）法则熟练后，解题过程可以适当简化．
例3 分析：（1）题的底数不同，首先应化为同底数幂，把![](https://wkrtcs.bdimg.com/rtcs/image?w=87&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"87","h":"23","dataType":"gif","c":"word/media/image26.png"})
视作整体进行计算，（2）题先对除式进行乘方，把视作整体运用法则运算．
解：（1）
![](https://wkrtcs.bdimg.com/rtcs/image?w=271&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"271","h":"25","dataType":"gif","c":"word/media/image28.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=136&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"136","h":"41","dataType":"gif","c":"word/media/image29.png"})
(2) ![](https://wkrtcs.bdimg.com/rtcs/image?w=239&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"239","h":"28","dataType":"gif","c":"word/media/image30.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=261&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"261","h":"25","dataType":"gif","c":"word/media/image31.png"})
![](https://wkrtcs.bdimg.com/rtcs/image?w=71&md5sum=f5c6e576e4ae508eb79b2544d8af982a&sign=03bec9ab76&rtcs_flag=1&rtcs_ver=3.1&l=webapp&bucketNum=6&ipr={"t":"img","w":"71","h":"25","dataType":"gif","c":"word/media/image32.png"})
说明：多项式因式如果互为相反数时，注意符号．
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