指數定侓,10分!!快入!!

指數
若a不等於0，
1.(am)(an)=am+n
2.(am)/(an)=am-n
3.(am)n=amn
4.a0=1
5.a-n=1/(an)
6.(ab)n=(an)(bn)
7.(a/b)n=(an)/(bn)

(1)(4xy/5y2)2[10xy/(2x2)]
=16x2y2/25y4×10xy/4x2
=160x3y3/100x2y4
=8x/5y

2.(ab)(2a2b)(3a3b2)2/18a4b7
=(ab)(2a2b)(9a6b4)/18a4b7
=(2a3b2)(9a6b4)/18a4b7
=18a9b6/18a4b7
=a4/b

3.(3uv)(u2v)2(uv2)3/(2u2v2)4
=(3uv)(u4v2)(u3v6)/(16u8v8)
=(3u8v9)/(16u8v8)
=3v/16

負指數:
4.(3a-2b)-2
=3-2a-2×-2b-2
=(1/32)(a4)(b-2)
　a4
=-------
　9b2

5. (4^-1 - 6^-1)^-1 = (1/4 - 1/6)^-1 = (1/12)^-1 = 12

6) (-2^-2)^-3 = [1/(-2)^2]^-3 = (1/4)^-3 = 4^3 = 64

7 (-(5/4))^3 = (-1)^3*(5/4)^3 = -125/64


指數方程:
1. 9(3^x+1)=27^2x
9[3^(x+1)]=27^2x
3^(x+2)=3^6x
6x=x+2
x = 2/5
2. 4^(x+1)+4^x - 4^(x-1)=19
4^(x+1)+4^x-4^(x-1)=19
4(4^x) + 4^x - 4^x ÷4 = 19
(4+1-0.25)4^x = 19
4^x = 4
x = 1

3. 6^(x+2)-2(6^x+1)-12(6^x)=2
6^(x+2)-2[6^(x+1)]-12(6^x)=2
36(6^x) - 12(6^x) -12(6^x) = 2
12(6^x) = 2
6^x = 1/6
6^x = 6^(-1)
x = -1
4. 3^2x -12(3^x)+27=0
3^2x-12(3^x)+27=0
9(3^x) - 12(3^x) + 27 = 0
-3(3^x) +27 = 0
3^x = 9
x = 2


.(x2n+1+x2n-2)/(x2n+3+x2n+1)
= [x ‧x2n+ x2‧ x2n ]/ [(x3‧x2n)+ x‧x2n ]
= (x + x2) x2n / [(x3 + x) x2n ]
= (x + x2) / (x3 + x)
= x (1 + x) / [ x (x2 +1) ]
= (1 + x) / (x2+1)

33d. 2xn+3﹣x2n/ x2n+3﹣2xn+6
={xn[2x3﹣xn]}/{xn[xn+3)﹣2x6]}
=[2x3﹣xn]/[xn+3﹣2x6]
=[2-xn-3]/[xn﹣2x3]
=[2-xn-3]/{(x3)[xn-3﹣2]}
= -1/x^3

其它的練習可到以下網址：
www.mfbmclct.edu.hk/~maths/Teaching%20Schedule/Sc2...

haofuwei.myweb.hinet.net/Lecture%20notes/V2/sv1ch1...

http://hk.wrs.yahoo.com/_ylt=A8tU33CdVQNHeHQAqGGzygt.;_ylu=X3oDMTB2dW8yNmN0BGNvbG8DdwRsA1dTMQRwb3MDOQRzZWMDc3IEdnRpZAM-/SIG=124hfq3tq/EXP=1191487261/**http%3A//csm00.csu.edu.tw/0166/2005calculus/26.htm

書有很多例子，你想要的是那些例子？

我想例子未必需要，但我建議你可以用以下的「拍檔」：
首先你要知2的3次是8，2的4次是16
要計算例如a^m * a^n 時，可以用代入法找答案，在這題可得128，再用計數機得5，便能重組答案為a^(m+n)

其他定律亦一樣。