✔ 最佳答案
1.
(3^344)^8 * (1/27)^890
= (3^344)^8 * [3^(-3)]^890
= 3^(344*8) * 3^(-3*890)
= 3^2752 * 3^(-2670)
= 3^(2752-2670)
= 3^82
≈ 1.33 x 10^39 (三位有效數字)
*****
2.
(-2)^719 * (0.5)^721
= -2^719 * [2^(-1)]^721
= -2^719 * 2^(-1*721)
= -2^719 * 2^(-721)
= -2^(719-721)
= -2^(-2)
= -(1/2^2)
= -1/4
*****
3.
3^911 * (-1/3)^912
= 3^911 * (3^-1)^912
= 3^911 * 3^(-912)
= 3^(911 - 912)
= 3^(-1)
= 1/3
*****
4.
(1/8)^400 * (2^400)^5
= [2^(-3)]^400 * (2^400)^5
= 2^(-3*400) * 2^(400*5)
= 2^(-1200) * 2(2000)
= 2^(-1200+2000)
= 2^800
= 6.67 * 10^240
*****
5.
x² - (3 + q)x + q ≡ (x-p)(x+4)+33
x² - (3 + q)x + q ≡ x² + (4 -p)x + (33 - 4p)
兩邊的 x 項相等：
-(3 + q) = 4 - p
-3 - q = 4 - p
p - q = 7 ...... [1]
兩的常數項相等：
q = 33 - 4p
4p + q = 33 ...... [2]
[1] + [2] :
5p = 40
p = 8
把 p = 8 代入 [1] 中：
(8) - q = 7
q = 1
所以 p = 8, q = 1
*****
6.
解法一：
x² - 2r ≡ (x + 3)(x - s) - 7
x² - 2r ≡ x² + (3 - s)x - (3s + 7)
兩邊的 x 項相等：
3 - s = 0
s = 3
兩邊的常數項相等：
-2r = -(3s + 7)
-2r = -[3(3) + 7]
-2r = -16
r = 8
解法二：
x² - 2r ≡ (x + 3)(x - s) - 7
令 x = -3 :
(-3)² - 2r = -7
9 - 2r = -7
2r = 16
r = 8
*****
7.
解法一：
a(x - 1)² + b(2x - 4)² ≡ 4x² - 32x + 40
a(x² - 2x + 1) + b(4x² - 16x + 16) ≡ 4x² - 32x + 40
(a + 4b)x² - (2a + 16b) + (a + 16b) ≡ 4x² - 32x + 40
兩邊x² 項相等：
a + 4b = 4 ...... [1]
兩邊常數項相等：
a + 16b = 40 ...... [2]
[2] - [1] :
12b = 36
b = 3
解法二：
a(x - 1)² + b(2x - 4)² ≡ 4x² - 32x + 40
令 x = 1 :
b[2(1) - 4]² = 4(1)² - 32(1) + 40
4b = 12
b = 3
*****
2012-12-31 21:12:17 補充：
1. 題目更正後：
(3^334)^8 * (1/27)^890
= 3^(334)^8 * [3^(-3)]^890
= 3^(334*8) * 3^(-3*890)
= 3^2672 * 3^(*-2670)
= 3^(2672-2670)
= 3^2
= 9 ...... (答案)
