(3question) Laws of indices

您好，我是 lop，高興能解答您的問題。

(1)

x^a = 3 --- (1)
x^b = 12 --- (2)

(1) × (2) :

(x^a)(x^b) = 3(12)
x^(a+b) = 36

D

(2)

3x(x^(m-1)+7) = 3x^m+18
x(x^(m-1)+7) = x^m + 6
7x + x[x^(m-1)] = x^m + 6
7x + x^(m-1+1) = x^m + 6
7x + x^m = x^m + 6
7x = 6
x = 6/7

(3)

[(-1)^n](xy) + [(-1)^n+1](xy)
= [(-1)^n](xy) + [(-1)^n](xy) + xy
= (2xy)[(-1)^n] + xy

Since n is a nature number , (-1)^n must be 1 or -1 ,

(2xy)[(-1)^n] + xy
= -2xy + xy or 2xy + xy
= -xy or 3xy

None of above

2011-12-25 17:02:12 補充：
(3)

[(-1)^n](xy) + [(-1)^(n+1)](xy)
= [(-1)^n](xy) + (-1)[(-1)^n](xy)
= [(-1)^n](xy) - [(-1)^n](xy)
= 0

A

3) (-1)^n xy + (-1)^(n+1) xy
= (-1)^n xy[1 + (-1)] ~ By taking out the common factor (-1)^n xy
= (-1)^n xy(0)
= 0
Ans: A