1. 以a*m/n的形式表示下列各題，其中m、n為整數及n不等於0。
a. ^5平方根a b. ^4平方根a^3
c. (^3平方根a)^4 d. 1/^3平方根a
2. 化簡下列各式，並以正指數表示答案。
a. 平方根b*^3平方根b b. ^3平方根27b^-6
c. 平方根b平方根b d. (b/^3平方根b)^-3
3. 化簡下列各式。
a. ^3平方根-343 b. (^3平方根27)^-2
c. ^5平方根32^3 d. (平方根2又1/4)^-1
4. 化簡下列各式。
a. 25^3/2 b. 81^-3/4
c. (-125)^2/3 d. (6^-2)^1/2
5. 化簡下列各式。
a. ^3平方根125-^3平方根-125 b. 8^-1/3+^3平方根27^-2
c. 平方根0.009^3+^3平方根0.027 d. 24*(^5平方根32)^-3
指數及對數函數（１）
2007-11-07 7:01 am
回答 (3)
2007-11-09 3:42 am
✔ 最佳答案
1a.5√a= a1/5
b. 4√a3
= (a3)1/4
= a3/4
c. (3√a)4
= (a1/3)4
= a4/3
d. 1/3√a
= 1/a1/3
= a-1/3
2a.√b‧3√b
= b1/2‧(b)1/3
= b(1/2)+(1/3)
= b5/6
b. 3√27b-6
= (27b-6)1/3
= (33b-6)1/3
= 3b-2
= 3/b2
c. √b√b
= √b‧b1/2
= √b1+(1/2)
= √b3/2
= (b3/2)1/2
= b3/4
d. (b/3√b)-3
= (b/b1/3)-3
= b-3/b-1
= 1/b-1-(-3)
= 1/b2
3a. 3√-343
= 3√-73
= ( -73)1/3
= -7
b. (3√27)-2
= (3√33)-2
= [(33)1/3]-2
= (3)-2
= 1/32
= 1/9
c.5√323
= 5√(25)3
= 5√215
= (215)1/5
= 23
= 8
d.(√9/4)-1
= [(9/4)1/2]-1
= (3/2)-1
= 2/3
4a. 253/2
= (52)3/2
= 53
= 125
b. 81-3/4
= (34)-3/4
= 3-3
= 1/33
= 1/27
c. (-125)2/3
= (-53)2/3
= (-5)2
= 25
d.(6-2)1/2
= 6-1
= 1/6
5a.3√125﹣3√-125
= 3√53﹣3√-53
= (53)1/3﹣(-53)1/3
= 5﹣(-5)
= 10
b. 8-1/3 + 3√27-2
= (23)-1/3 + [(33)-2]1/3
= 2-1 + 27-6/3
= (1/2) + (1/729)
= 731/1458
c. √0.093+3√0.027
= [(0.32)3]1/2+(0.33)1/3
= (0.36)1/2+0.3
= 0.33+0.3
= 0.027+0.3
= 0.027+0.3
= 0.327
d.24(5√32)-3
= 24[(25)1/5]-3
= 24(2)-3
= 24(1/8)
= 3
2007-11-10 9:11 pm
1a.5√a
= a1/5
b. 4√a3
= (a3)1/4
= a3/4
c. (3√a)4
= (a1/3)4
= a4/3
d. 1/3√a
= 1/a1/3
= a-1/3
2a.√b‧3√b
= b1/2‧(b)1/3
= b(1/2)+(1/3)
= b5/6
b. 3√27b-6
= (27b-6)1/3
= (33b-6)1/3
= 3b-2
= 3/b2
c. √b√b
= √b‧b1/2
= √b1+(1/2)
= √b3/2
= (b3/2)1/2
= b3/4
d. (b/3√b)-3
= (b/b1/3)-3
= b-3/b-1
= 1/b-1-(-3)
= 1/b2
3a. 3√-343
= 3√-73
= ( -73)1/3
= -7
b. (3√27)-2
= (3√33)-2
= [(33)1/3]-2
= (3)-2
= 1/32
= 1/9
c.5√323
= 5√(25)3
= 5√215
= (215)1/5
= 23
= 8
d.(√9/4)-1
= [(9/4)1/2]-1
= (3/2)-1
= 2/3
4a. 253/2
= (52)3/2
= 53
= 125
b. 81-3/4
= (34)-3/4
= 3-3
= 1/33
= 1/27
c. (-125)2/3
= (-53)2/3
= (-5)2
= 25
d.(6-2)1/2
= 6-1
= 1/6
5a.3√125﹣3√-125
= 3√53﹣3√-53
= (53)1/3﹣(-53)1/3
= 5﹣(-5)
= 10
b. 8-1/3 + 3√27-2
= (23)-1/3 + [(33)-2]1/3
= 2-1 + 27-6/3
= (1/2) + (1/729)
= 731/1458
c. √0.093+3√0.027
= [(0.32)3]1/2+(0.33)1/3
= (0.36)1/2+0.3
= 0.33+0.3
= 0.027+0.3
= 0.027+0.3
= 0.327
d.24(5√32)-3
= 24[(25)1/5]-3
= 24(2)-3
= 24(1/8)
= 3
= a1/5
b. 4√a3
= (a3)1/4
= a3/4
c. (3√a)4
= (a1/3)4
= a4/3
d. 1/3√a
= 1/a1/3
= a-1/3
2a.√b‧3√b
= b1/2‧(b)1/3
= b(1/2)+(1/3)
= b5/6
b. 3√27b-6
= (27b-6)1/3
= (33b-6)1/3
= 3b-2
= 3/b2
c. √b√b
= √b‧b1/2
= √b1+(1/2)
= √b3/2
= (b3/2)1/2
= b3/4
d. (b/3√b)-3
= (b/b1/3)-3
= b-3/b-1
= 1/b-1-(-3)
= 1/b2
3a. 3√-343
= 3√-73
= ( -73)1/3
= -7
b. (3√27)-2
= (3√33)-2
= [(33)1/3]-2
= (3)-2
= 1/32
= 1/9
c.5√323
= 5√(25)3
= 5√215
= (215)1/5
= 23
= 8
d.(√9/4)-1
= [(9/4)1/2]-1
= (3/2)-1
= 2/3
4a. 253/2
= (52)3/2
= 53
= 125
b. 81-3/4
= (34)-3/4
= 3-3
= 1/33
= 1/27
c. (-125)2/3
= (-53)2/3
= (-5)2
= 25
d.(6-2)1/2
= 6-1
= 1/6
5a.3√125﹣3√-125
= 3√53﹣3√-53
= (53)1/3﹣(-53)1/3
= 5﹣(-5)
= 10
b. 8-1/3 + 3√27-2
= (23)-1/3 + [(33)-2]1/3
= 2-1 + 27-6/3
= (1/2) + (1/729)
= 731/1458
c. √0.093+3√0.027
= [(0.32)3]1/2+(0.33)1/3
= (0.36)1/2+0.3
= 0.33+0.3
= 0.027+0.3
= 0.027+0.3
= 0.327
d.24(5√32)-3
= 24[(25)1/5]-3
= 24(2)-3
= 24(1/8)
= 3
參考: 自己&別人
2007-11-08 1:49 am
1
a.)a^5/2
b.)a^6
c)a^6
d)a^(-3/2)
2
a.)b^2
b.)27^(3/2)*b^(-9)
c.)b
d.)b^3/2
3
a.)開方負號？＝ ＝
b.)3^(-9)=1/19683
c.)32^15/2
d.)2/3
4
a.)5^3=125
b.)3^(-3)=1/27
c.)(-1)125^2=-15625
d.)6^(-1)=1/6
2007-11-07 18:00:28 補充：
ｓｏｒ= = 錯曬 好多題啊 唔做ｌａ 食飯先
a.)a^5/2
b.)a^6
c)a^6
d)a^(-3/2)
2
a.)b^2
b.)27^(3/2)*b^(-9)
c.)b
d.)b^3/2
3
a.)開方負號？＝ ＝
b.)3^(-9)=1/19683
c.)32^15/2
d.)2/3
4
a.)5^3=125
b.)3^(-3)=1/27
c.)(-1)125^2=-15625
d.)6^(-1)=1/6
2007-11-07 18:00:28 補充：
ｓｏｒ= = 錯曬 好多題啊 唔做ｌａ 食飯先
收錄日期: 2021-04-13 21:23:33
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https://hk.answers.yahoo.com/question/index?qid=20071106000051KK04457