f.3maths 題

As follows~

圖片參考：http://i248.photobucket.com/albums/gg191/ncy_0916/maths30.jpg?t=1217922562


2008-08-05 15:50:32 補充：
根據指數定律，
a^m X a^n = a^(m + n)
a^m ÷ a^n = a^(m - n)
(a^m)^n = a^(mn)

2008-08-05 15:56:43 補充：
因為2^(2n) = 2^(n + n) = (2^n)(2^n)
指數定律：a^m X a^n = a^(m + n)

To get the answer stated, the expression should be written as:
{9(4^n) - 3[2^(n+1)]}/5[2^(n-1)].
For easy reading, let 2^n = x.
Therefore, 9(4^n) = 9x^2.
3[2^(n+1)] = 3[2x] = 6x.
2^(n-1) = x/2. Therefore, the expression becomes
(9x^2 - 6x)/[5(x/2)] = 2x(9x - 6)/5x = (18x - 12)/5 = [18(2^n) - 12]/5.