化簡整數指數,快,快,快,快,急,40marks!!!!!!!!

1)16a^2/12x^2÷(8a^3b^3/9x^3y^2)
=(16a^2)(9x^3y^2)/(12x^2)(8a^3b^3)
=(144/96)[a^(2-3)x^(3-2)y^2/b^3]
=(3/2)xy^2/(ab^3)
=3xy^2/2ab^3

2)( -2a ^3)^2(3ab^2)^4
=( -2a ^3)^2(3ab^2)^4
=(4a^6)(81a^4b^8)
=(4/81)[a^(6+4)b^8]
=(4/81)(a^10b^8)

3)(25^3n×5^n-1/125^2n+1)
=(25^3n×5^n-1/125^2n+1)
=[5^2(3n)x5^(n-1)/5^3(2n+1)]
=[5^(6n+n-1-6n-3)]
=5^n-4

4)8^n+1-8^n/2^3n-1
=[2^3(n+1)-2^3n]/2^3n-1
=2^3n+1/2^3n-1-2^3n/2^3n-1
=2^(3n+1-3n+1)-2^(3n-3n+1)
=2^2-2^1
=4-2
=2

2007-09-29 14:35:08 補充：
係wo...第2條個係數應該係(4)(81)=324

2007-09-29 19:02:57 補充：
第四條第二步=2^3n+3/2^3n-1-2^3n/2^3n-1=2^(3n+3-3n+1)-2^(3n-3n+1)=2^4-2^1=16-2=14

1)16a^2/12x^2÷(8a^3b^3/9x^3y^2)
=(144/96)[a^(2-3)x^(3-2)y^2/b^3]
=(3/2)xy^2/(ab^3)
=3xy^2/2ab^3

2)( -2a ^3)^2(3ab^2)^4
=(4a^6)(81a^4b^8)
=(4)(81)[a^(6+4)b^8]
=324(a^10b^8)

3)(25^3n×5^n-1/125^2n+1)
=[5^2(3n)x5^(n-1)/5^3(2n+1)]
=[5^(6n+n-1-6n-3)]
=5^n-4

2007-09-29 19:47:13 補充：
4) 8^n+1-8^n/2^3n-1=2^3n+3/2^3n-1-2^3n/2^3n-1=2^(3n+3-3n+1)-2^(3n-3n+1)=2^4-2^1=16-2=14

第一題的(b63)是否應該是(b^3)：
(16a^2/12x^2)÷(8a^3b^3/9x^3y^2)
=(16a^2 * 9x^3 y^2 )/(12x^2 * 8a^3 b^3)
=1.5 a^(2-3) x^(3-2) y^2 b^-3
=1.5 a^-1 x y^2 b^-3

( -2a ^3)^2(3ab^2)^4
=(4a^6)*(81a^4 b^8)
=324 a^(6+4) b^8
=324 a^10 b^8

25^3n×5^n-1/125^2n+1
=5^6n * 5^n-1 / 5*6n+3
=5^(6n+n-1-6n-3)
=5^(n-4)

最後一題按你打的是：
8^n+1-8^n/2^3n-1
=2^(3n+3) -2^3n / 2^(3n-1)
=2^(3n+3) -2^(3n-3n+1)
=2^(3n+3) -2

或許最後一題你是想這樣表達：
[8^n+1 -8^n]/2^3n-1
=[2^(3n+3) -2^3n] / 2^(3n-1)
=2^(3n+3-3n+1) -2^(3n-3n+1)
=2^4 -2^1
=16-1
=15

2007-09-29 13:46:29 補充：
樓上的第2及第4題都出了mistake^^"

2007-09-29 22:25:13 補充：
哎呀...自己都出問題添-.-第四題最後一步係16-2=14-.-

「^」點解？