第四章指數(shù)涵數(shù)與對數(shù)函數(shù)第四章14.1整數(shù)指數(shù)冪1.整數(shù)指數(shù)冪的概念當(dāng)n為正整數(shù)時,n個相同因數(shù)a的相乘,記作:an,稱為正整數(shù)指數(shù)冪,讀作“a的n次方”,也可讀作“a的n次冪”,其中,a稱為底數(shù),n稱為指數(shù)令當(dāng)門=0時,a(a≠0)稱為零指數(shù)冪;任何不等于0的數(shù)的0次冪都等于1即a0=1(a≠0)令形如an(a≠0)稱為負(fù)整數(shù)指數(shù)冪;an是an的倒數(shù)令正整數(shù)指數(shù)冪,零指數(shù)冪,負(fù)整數(shù)指數(shù)冪合稱為整數(shù)指數(shù)冪.4.1整數(shù)指數(shù)冪24.1整數(shù)指數(shù)冪2.整數(shù)指數(shù)冪運(yùn)算法則整數(shù)指數(shù)冪運(yùn)算法則(a≠0,b≠0,m,n為整數(shù))am×a=am+(am)(aby=a"b練習(xí):小試牛刀:比一比,看誰算的快4.1整數(shù)指數(shù)冪34.1整數(shù)指數(shù)冪鞏固知識1.整數(shù)指數(shù)冪的概念2.整數(shù)指數(shù)冪運(yùn)算法則課后練習(xí)練習(xí)冊334.1整數(shù)指數(shù)冪44.2有理指數(shù)冪1.次根式的定義如果x2=a(a≥0),則稱x為a的平方根(二次方根),記作:X=±a如果x3=a,則稱x為a的立方根(三次方根),記作:x=3a如果ⅹ=a(n是一個大于1的正整數(shù)),則稱x為a的一個n方次根,記作:x=a當(dāng)n為奇數(shù)時,正數(shù)的n次方根是一個正數(shù),負(fù)數(shù)的n次方根是一個負(fù)數(shù)當(dāng)n為偶數(shù)時,對于每一個正數(shù)a的n次方根有兩個,它們互為相反數(shù),分別用na和-na表示,可以合并寫為“±G>0)”4.2有理指數(shù)冪542有理指數(shù)冪而對于每一個負(fù)數(shù)a,它的偶次方根是沒有意義的;零的n次方根是零,用n0=0表示;我們把形如n(有意義時)的式子稱為n次根式,其中為根指數(shù),a稱為被開方數(shù)性質(zhì)根據(jù)n次方根的意義,可得當(dāng)為奇數(shù)時a=a(a)=a當(dāng)為偶數(shù)時a=a=-a(a<0,≥0)42有理指數(shù)冪642有理指數(shù)冪【例1】求下列各式的值÷18)2√1023的3-4√a-b)2(a≤b)解(1)8)=8令(2)√-102=-10=10(3)3-x+2=3-x(4)V(a-b)2=a-b=b-a(a<b)42有理指數(shù)冪742有理指數(shù)冪令2.有理指數(shù)冪的定義正數(shù)的正分?jǐn)?shù)指數(shù)冪的意義是:冷a=ama>0,m,且neN)÷正數(shù)的負(fù)分?jǐn)?shù)指數(shù)冪:a=1(a>0,m,n∈N且n>1)令規(guī)定了分?jǐn)?shù)指數(shù)冪的意義以后,指數(shù)從整數(shù)推廣到了有理數(shù),即分?jǐn)?shù)指數(shù)冪是有理指數(shù)冪42有理指數(shù)冪842有理指數(shù)冪【例2】求下列各式的值:183210023(16解(1)g5=(23令(2)1002100203210令(3)27小試牛刀142有理指數(shù)冪942有理指數(shù)冪【例3】化簡下列各式:÷123×.5×922(p248)33(5-、125)÷54列2()解(1)2×52=2×3x號7×1252×32×(3×2-)3×(22×3)62×32×3x2%×2x32×23×23×32×33×30=2×233×32362×3=642有理指數(shù)冪10指數(shù)函數(shù)與對數(shù)函數(shù)課件11指數(shù)函數(shù)與對數(shù)函數(shù)課件12指數(shù)函數(shù)與對數(shù)函數(shù)課件13指數(shù)函數(shù)與對數(shù)函數(shù)課件14指數(shù)函數(shù)與對數(shù)函數(shù)課件15指數(shù)函數(shù)與對數(shù)函數(shù)課件16指數(shù)函數(shù)與對數(shù)函數(shù)課件17指數(shù)函數(shù)與對數(shù)函數(shù)課件18指數(shù)函數(shù)與對數(shù)函數(shù)課件19指數(shù)函數(shù)與對數(shù)函數(shù)課件20指數(shù)函數(shù)與對數(shù)函數(shù)課件21指數(shù)函數(shù)與對數(shù)函數(shù)課件22指數(shù)函數(shù)與對數(shù)函數(shù)課件23指數(shù)函數(shù)與對數(shù)函數(shù)課件24指數(shù)函數(shù)與對數(shù)函數(shù)課件25指數(shù)函數(shù)與對數(shù)函數(shù)課件26指數(shù)函數(shù)與對數(shù)函數(shù)課件27指數(shù)函數(shù)與對數(shù)函數(shù)課件28指數(shù)函數(shù)與對數(shù)函數(shù)課件29指數(shù)函數(shù)與對數(shù)函數(shù)課件30指數(shù)函數(shù)與對數(shù)函數(shù)課件31指數(shù)函數(shù)與對數(shù)函數(shù)課件32指數(shù)函數(shù)與對數(shù)函數(shù)課件33指數(shù)函數(shù)與對數(shù)函數(shù)課件34指數(shù)函數(shù)與對數(shù)函數(shù)課件35指數(shù)函數(shù)與對數(shù)函數(shù)課件36指數(shù)函數(shù)與對數(shù)函數(shù)課件37指數(shù)函數(shù)與對數(shù)函數(shù)課件38指數(shù)函數(shù)與對數(shù)函數(shù)課件39指數(shù)函數(shù)與對數(shù)函數(shù)課件40指數(shù)函數(shù)與對數(shù)函數(shù)課件41指數(shù)函數(shù)與對數(shù)函數(shù)課件42指數(shù)函數(shù)與對數(shù)函數(shù)課件43指數(shù)函數(shù)與對數(shù)函數(shù)課件44指數(shù)函數(shù)與對數(shù)函數(shù)課件45指數(shù)函數(shù)與對數(shù)函數(shù)課件46指數(shù)函數(shù)與對數(shù)函數(shù)課件47指數(shù)函數(shù)與對數(shù)函數(shù)課件48指數(shù)函數(shù)與對數(shù)函數(shù)課件49指數(shù)函數(shù)與對數(shù)函數(shù)課件50指數(shù)函數(shù)與對數(shù)函數(shù)課件51指數(shù)函數(shù)與對數(shù)函數(shù)課件52指數(shù)函數(shù)與對數(shù)函數(shù)課件53指數(shù)函數(shù)與對數(shù)函數(shù)課件54指數(shù)函數(shù)與對數(shù)函數(shù)課件55指數(shù)函數(shù)與對數(shù)函數(shù)課件56指數(shù)函數(shù)與對數(shù)函數(shù)課件57指數(shù)函數(shù)與對數(shù)函數(shù)課件58指數(shù)函數(shù)與對數(shù)函數(shù)課件59指數(shù)函數(shù)與對數(shù)函數(shù)課件60指數(shù)函數(shù)與對數(shù)函數(shù)課件61指數(shù)函數(shù)與對數(shù)函數(shù)課件62指數(shù)函數(shù)與對數(shù)函數(shù)課件63指數(shù)函數(shù)與對數(shù)函數(shù)課件64指數(shù)函數(shù)與對數(shù)函數(shù)課件65指數(shù)函數(shù)與對數(shù)函數(shù)課件66指數(shù)函數(shù)與對數(shù)函數(shù)課件67指數(shù)函數(shù)與對數(shù)函數(shù)課件68指數(shù)函數(shù)與對數(shù)函數(shù)課件69指數(shù)函數(shù)與對數(shù)函數(shù)課件70指數(shù)函數(shù)與對數(shù)函數(shù)課件71第四章指數(shù)涵數(shù)與對數(shù)函數(shù)第四章724.1整數(shù)指數(shù)冪1.整數(shù)指數(shù)冪的概念當(dāng)n為正整數(shù)時,n個相同因數(shù)a的相乘,記作:an,稱為正整數(shù)指數(shù)冪,讀作“a的n次方”,也可讀作“a的n次冪”,其中,a稱為底數(shù),n稱為指數(shù)令當(dāng)門=0時,a(a≠0)稱為零指數(shù)冪;任何不等于0的數(shù)的0次冪都等于1即a0=1(a≠0)令形如an(a≠0)稱為負(fù)整數(shù)指數(shù)冪;an是an的倒數(shù)令正整數(shù)指數(shù)冪,零指數(shù)冪,負(fù)整數(shù)指數(shù)冪合稱為整數(shù)指數(shù)冪.4.1整數(shù)指數(shù)冪734.1整數(shù)指數(shù)冪2.整數(shù)指數(shù)冪運(yùn)算法則整數(shù)指數(shù)冪運(yùn)算法則(a≠0,b≠0,m,n為整數(shù))am×a=am+(am)(aby=a"b練習(xí):小試牛刀:比一比,看誰算的快4.1整數(shù)指數(shù)冪744.1整數(shù)指數(shù)冪鞏固知識1.整數(shù)指數(shù)冪的概念2.整數(shù)指數(shù)冪運(yùn)算法則課后練習(xí)練習(xí)冊334.1整數(shù)指數(shù)冪754.2有理指數(shù)冪1.次根式的定義如果x2=a(a≥0),則稱x為a的平方根(二次方根),記作:X=±a如果x3=a,則稱x為a的立方根(三次方根),記作:x=3a如果ⅹ=a(n是一個大于1的正整數(shù)),則稱x為a的一個n方次根,記作:x=a當(dāng)n為奇數(shù)時,正數(shù)的n次方根是一個正數(shù),負(fù)數(shù)的n次方根是一個負(fù)數(shù)當(dāng)n為偶數(shù)時,對于每一個正數(shù)a的n次方根有兩個,它們互為相反數(shù),分別用na和-na表示,可以合并寫為“±G>0)”4.2有理指數(shù)冪7642有理指數(shù)冪而對于每一個負(fù)數(shù)a,它的偶次方根是沒有意義的;零的n次方根是零,用n0=0表示;我們把形如n(有意義時)的式子稱為n次根式,其中為根指數(shù),a稱為被開方數(shù)性質(zhì)根據(jù)n次方根的意義,可得當(dāng)為奇數(shù)時a=a(a)=a當(dāng)為偶數(shù)時a=a=-a(a<0,≥0)42有理指數(shù)冪7742有理指數(shù)冪【例1】求下列各式的值÷18)2√1023的3-4√a-b)2(a≤b)解(1)8)=8令(2)√-102=-10=10(3)3-x+2=3-x(4)V(a-b)2=a-b=b-a(a<b)42有理指數(shù)冪7842有理指數(shù)冪令2.有理指數(shù)冪的定義正數(shù)的正分?jǐn)?shù)指數(shù)冪的意義是:冷a=ama>0,m,且neN)÷正數(shù)的負(fù)分?jǐn)?shù)指數(shù)冪:a=1(a>0,m,n∈N且n>1)令規(guī)定了分?jǐn)?shù)指數(shù)冪的意義以后,指數(shù)從整數(shù)推廣到了有理數(shù),即分?jǐn)?shù)指數(shù)冪是有理指數(shù)冪42有理指數(shù)冪7942有理指數(shù)冪【例2】求下列各式的值:183210023(16解(1)g5=(23令(2)1002100203210令(3)27小試牛刀142有理指數(shù)冪8042有理指數(shù)冪【例3】化簡下列各式:÷123×.5×922(p248)33(5-、125)÷54列2()解(1)2×52=2×3x號7×1252×32×(3×2-)3×(22×3)62×32×3x2%×2x32×23×23×32×33×30=2×233×32362×3=642有理指數(shù)冪81指數(shù)函數(shù)與對數(shù)函數(shù)課件82指數(shù)函數(shù)與對數(shù)函數(shù)課件83指數(shù)函數(shù)與對數(shù)函數(shù)課件84指數(shù)函數(shù)與對數(shù)函數(shù)課件85指數(shù)函數(shù)與對數(shù)函數(shù)課件86指數(shù)函數(shù)與對數(shù)函數(shù)課件87指數(shù)函數(shù)與對數(shù)函數(shù)課件88指數(shù)函數(shù)與對數(shù)函數(shù)課件89指數(shù)函數(shù)與對數(shù)函數(shù)課件90指數(shù)函數(shù)與對數(shù)函數(shù)課件91指數(shù)函數(shù)與對數(shù)函數(shù)課件92指數(shù)函數(shù)與對數(shù)函數(shù)課件93指數(shù)函數(shù)與對數(shù)函數(shù)課件94指數(shù)函數(shù)與對數(shù)函數(shù)課件95指數(shù)函數(shù)與對數(shù)函數(shù)課件96指數(shù)函數(shù)與對數(shù)函數(shù)課件97指數(shù)函數(shù)與對數(shù)函數(shù)課件98指數(shù)函數(shù)與對數(shù)函數(shù)課件99指數(shù)函數(shù)與對數(shù)函數(shù)課件100指數(shù)函數(shù)與對數(shù)函數(shù)課件101指數(shù)函數(shù)與對數(shù)函數(shù)課件102指數(shù)函數(shù)與對數(shù)函數(shù)課件103指數(shù)函數(shù)與對數(shù)函數(shù)課件104指數(shù)函數(shù)與對數(shù)函數(shù)課件105指數(shù)函數(shù)與對數(shù)函數(shù)課件106指數(shù)函數(shù)與對數(shù)函數(shù)課件107指數(shù)函數(shù)與對數(shù)函數(shù)課件108指數(shù)函數(shù)與對數(shù)函數(shù)課件109指數(shù)函數(shù)與對數(shù)函數(shù)課件110指數(shù)函數(shù)與對數(shù)函數(shù)課件111指數(shù)函數(shù)與對數(shù)函數(shù)課件112指數(shù)函數(shù)與對數(shù)函數(shù)課件113指數(shù)函數(shù)與對數(shù)函數(shù)課件114指數(shù)函數(shù)與對數(shù)函數(shù)課件115指數(shù)函數(shù)與對數(shù)函數(shù)課件116指數(shù)函數(shù)與對數(shù)函數(shù)課件117指數(shù)函數(shù)與對數(shù)函數(shù)課件118指數(shù)函數(shù)與對數(shù)函數(shù)課件119指數(shù)函數(shù)與對數(shù)函數(shù)課件120指數(shù)函數(shù)與對數(shù)函數(shù)課件121指數(shù)函數(shù)與對數(shù)函數(shù)課件122指數(shù)函數(shù)與對數(shù)函數(shù)課件123指數(shù)函數(shù)與對數(shù)函數(shù)課件124指數(shù)函數(shù)與對數(shù)函數(shù)課件125指數(shù)函數(shù)與對數(shù)函數(shù)課件126指數(shù)函數(shù)與對數(shù)函數(shù)課件127指數(shù)函數(shù)與對數(shù)函數(shù)課件128指數(shù)函