1、-1-第三章基本初等函数()-2-3 3.1 1指数与指数函数-3-3 3.1 1.1 1实数指数幂及其运算-4-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1.理解有理指数幂的含义,会用幂的运算法则进行有关计算.2.通过具体实例了解实数指数幂的意义.3.通过本节的学习,进一步体会“用有理数逼近无理数”的思想,可以利用计算器或计算机实际操作,感受“逼近”的过程.-5-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNA
2、N JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航12341.整数指数幂(2)正整指数幂的运算法则:aman=am+n;(am)n=amn;aman=am-n(mn,a0);(ab)n=anbn;-6-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234aman=am+n;(ab)n=anbn;(am)n=amn.同时,将指数的范围扩大到了整数.-7-3.1.1实数
3、指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234【做一做1-1】已知a0,m,n为整数,则下列各式中正确的有()B.anam=amnC.(an)m=am+nD.1an=a0-n解析:只有选项D是按照幂的运算法则进行运算的.选项A应为am-n,选项B应为am+n,选项C应为amn.答案:D-8-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典
4、例透析MUBIAODAOHANG目标导航1234【做一做1-2】化简:(a2b3)-2(a5b-2)0(a4b3)2的结果为.解析:原式=(a2)-2(b3)-21(a4)2(b3)2=a-4b-6a8b6=a-12b-12.答案:a-12b-12-9-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航12342.根式(2)n次方根的定义:如果存在实数x,使得xn=a(aR,n1,nN+),则x叫做a的n次方根.(3)n次方根的性质:在实数范围内
5、,正数的奇次方根是一个正数,负数的奇次方根是一个负数,零的奇次方根是零.设aR,n是大于1的奇数,则a的n次方根-10-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234-11-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234归纳总结归纳总结正数开方要分清,根指奇偶大不同,根指为奇
6、根一个,根指为偶双胞生.负数只有奇次根,算术方根零或正,正数若求偶次根,符号相反值相同.负数开方要慎重,根指为奇才可行,根指为偶无意义,零取方根仍为零.-12-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234-13-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234-14-3.1.
7、1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234答案:-8-15-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234(2)有理指数幂的运算法则:aa=a+(a0,Q);(a)=a(a0,Q);(ab)=ab(a0,b0,Q).-16-3.1.1实数指数幂及其运算ZHISHI SHULI知识
8、梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234名师点拨名师点拨0的正分数指数幂等于0,0的负分数指数幂没有意义,0的零指数幂也没有意义,有理指数幂的三条运算法则实际上可推广到实数指数幂.-17-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1234答案:D-18-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN
9、 JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航12434.无理指数幂教材中通过实例利用逼近的思想理解无理指数幂的意义.一般地,无理指数幂a(a0,是无理数)是一个确定的实数.另外,我们要熟记经常要用的公式:-19-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航-20-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦S
10、UITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航-21-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航-22-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航-23-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN
11、 JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航知识拓展知识拓展在进行幂和根式的化简时,一般是先将根式化成幂的形式,并化小数指数幂为分数指数幂,且尽可能地统一成分数指数幂的形式,再利用幂的性质进行化简、求值、计算,以利于运算,达到化繁为简的目的.对于根式的计算结果,并不强求统一的表示形式,一般用分数指数幂的形式来表示.如果有特殊要求,那么按要求给出结果,但结果中不能同时含有根号和分数指数幂,也不能既含有分母又含有负指数,即结果必须化为最简形式.-24-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHON
12、GNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-25-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-26-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG
13、目标导航题型一题型二题型三题型四题型五-27-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-28-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-29-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN
14、JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-30-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五反思反思在进行有关幂的运算时,要注意化归思想的运用;另外化繁为简一直是我们解题的一条基本原则.熟悉幂的运算条件和幂的运算性质是正确解题的关键.-31-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理
15、ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-32-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-33-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAO
16、HANG目标导航题型一题型二题型三题型四题型五-34-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五分析:根据根式的性质进行化简.-35-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-36-3.1.1实数指数幂及其运算ZHISHI
17、 SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五反思反思在化简中需要开偶次方时,最好是先用绝对值表示开方的结果,再去掉绝对值,化简时要结合条件,有时应进行分类讨论.-37-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-38-3.1.1实数指数幂及其运算ZHISHI SHU
18、LI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-39-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-40-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUB
19、IAODAOHANG目标导航题型一题型二题型三题型四题型五反思反思通过本例题,我们能得到如下结论:(1)在分数指数幂中,若幂指数小于0,可先将其转化为正指数,再用公式化为根式.(2)当所化根式含有多重根号时,应先由里向外用分数指数幂的形式写出,然后进行化简.-41-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-42-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚
20、焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-43-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五分析:此题不宜采用直接求值的方法,要考虑把x+y及xy整体代入求值.-44-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TO
21、UXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五反思反思利用整体代入法求值注意以下几点:(1)注意对已知条件式的变形;(2)注意完全平方公式、平方差公式、立方差公式等的应用;(3)注意开方时对取值符号的讨论.-45-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-46-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYA
22、NLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-47-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-48-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-49-3
23、.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航题型一题型二题型三题型四题型五-50-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 6答案:A-51-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN
24、随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 62若a8=6(a0),则a等于()答案:C-52-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 6答案:A-53-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 6答案:44-54-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 6-55-3.1.1实数指数幂及其运算ZHISHI SHULI知识梳理ZHONGNAN JVJIAO重难聚焦SUITANGYANLIAN随堂演练DIANLI TOUXI典例透析MUBIAODAOHANG目标导航1 2 3 4 5 6
