數學題(中四-中五)

Ans:
D. -1/3

2014-01-02 18:39:41 補充：
(-3)^1299 x (1/3)^1300
=-[(3)^1299] x (1/3)^1300 ←∵次方为单數∴係-ve
=-[(3)^1299] /[(3)^1300] ←好簡單
=-[(3)^1299] /﹛[(3)^1299][3]﹜ ←分母:3^1300=(3^1299) x (3^1)
=-[1] /[3] ←約簡(3^1299)/(3^1299)=1
=-1/3

(-3)^1299 = [ - 1 x 3]^1299 = (-1)^1299 x 3^1299 = - 3^1299.
(1/3)^1300 = [ 3^(-1)]^1300 = 3^( -1300).
So their product = - 3^1299 x 3^( -1300) = - 3^(1299 - 1300) = - 3^( -1) = - 1/3.
Ans is D.