f3數學. 整數指數定律

1. a^n+4 - a^3n
------------------------
a^3n+3 - a^n+7

(a^n)( a^4) – (a^n)(a^n)(a^n)
------------------------------------------
(a^n)(a^n)(a^n)(a^3) – (a^n) (a^7)

(a^n)[( a^4) – (a^n)(a^n)]
-------------------------------------
(a^n)[(a^n)(a^n)(a^3) – (a^7)]

[( a^4) – (a^n)(a^n)]
-------------------------------
[(a^n)(a^n)(a^3) – (a^7)]

[( a^4) – (a^n)(a^n)]
-------------------------------------
[(a^n)(a^n)(a^3) – (a^3)(a^4)]

[( a^4) – (a^n)(a^n)]
-------------------------------------
(a^3) [(a^n)(a^n) – (a^4)]

- 1[(a^n)(a^n)- ( a^4) ]
--------------------------------
(a^3) [(a^n)(a^n) – (a^4)]

- 1
-------
(a^3)


2a,若n是正整數 , 證明 2^n x 3^n+1= 3．6^n

2^n x 3^n+1= 3．6^n

(2^n) (3^n) (3^1)= 3．6^n

(6^n)(3)= (3)(6^n)


2b,求 2^n x 3^n+1
       ------------------- 的值
            6^n-2

(2^n)(3^n)(3^1)
--------------------
(6^n)/(6^2)

(6^n)(3^1)
--------------------
(6^n)/(6^2)

(3^1)
------------
1/(6^2)

(3^1)(6^2)

(3)(36)

= 108

2^n x 3^n+1= 3．6^n
2^n x3^n x3^1=3x6^n
6^n................=6^n
____________________
2^n x 3^n+1/6^n-2
3x6^n/6^n x6^-2
3/(1/36)
108

2010-09-11 10:53:29 補充：
3^n+1=(3^n)(3^1)
_______________
6^n-2
(6^n)(6^-2)
6^n(1/36)

2010-09-11 10:54:02 補充：
2^n(3^n)=6^n