指數規則
指數規則，指數定律和例子。
什麼是指數
以a為底的n次方等於a的n次乘積：
a n = a × a × ... × a
n次
a 是底數，n 是指數。
例子
31 = 3
32 = 3 × 3 = 9
33 = 3 × 3 × 3 = 27
34 = 3 × 3 × 3 × 3 = 81
35 = 3 × 3 × 3 × 3 × 3 = 243
指數規則和屬性
| 規則名稱 | 規則 | 例子 |
|---|---|---|
| 產品規則 | a n ⋅ a m = a n+m | 2 3 ⋅ 2 4 = 2 3+4 = 128 |
| a n ⋅ b n = ( a ⋅ b ) n | 3 2 ⋅ 4 2 = (3⋅ 4) 2 = 144 | |
| 商規則 | a n / a m = a n - m | 2 5 / 2 3 = 2 5-3 = 4 |
| 一個n / b n = ( a / b ) n | 4 3 / 2 3 = (4/2) 3 = 8 | |
| 權力規則 | ( b n ) m = b n⋅m | (2 3 ) 2 = 2 3⋅2 = 64 |
| b n m = b ( n m ) | 2 3 2 = 2 ( 3 2 ) = 512 | |
| m √( b n ) = b n / m | 2 √(2 6 ) = 2 6/2 = 8 | |
| b 1/ n = n √ b | 8 1/3 = 3 √ 8 = 2 | |
| 負指數 | b -n = 1 / b n | 2 -3 = 1/2 3 = 0.125 |
| 零規則 | b 0 = 1 | 5 0 = 1 |
| 0 n = 0 , 對於n >0 | 0 5 = 0 | |
| 一條規則 | b 1 = b | 5 1 = 5 |
| 1 n = 1 | 1 5 = 1 | |
| 減一規則 |  |
(-1) 5 = -1 |
| 導數規則 | ( x n ) ' = n ⋅ x n -1 | ( x 3 ) ' = 3⋅ x 3-1 |
| 積分規則 | ∫ x n dx = x n +1 /( n +1)+ C | ∫ x 2 dx = x 2+1 /(2+1)+ C |
指數積規則
同底乘積法則
an ⋅ am = an+m
例子：
23 ⋅ 24 = 23+4 = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128
同指數乘積法則
an ⋅ bn = (a ⋅ b)n
例子：
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
請參閱：乘以指數
指數商規則
同底商法則
an / am = an-m
例子：
25 / 23 = 25-3 = 22 = 2⋅2 = 4
同指數商法則
an / bn = (a / b)n
例子：
43 / 23 = (4/2)3 = 23 = 2⋅2⋅2 = 8
參見：指數除法
指數冪規則
冪律一
(an) m = a n⋅m
例子：
(23)2 = 23⋅2 = 26 = 2⋅2⋅2⋅2⋅2⋅2 = 64
冪律 II
a nm = a (nm)
例子：
232 = 2(32) = 2(3⋅3) = 29 = 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2 = 512
自由基的冪律
m√(a n) = a n/m
例子：
2√(26) = 26/2 = 23 = 2⋅2⋅2 = 8
負指數規則
b-n = 1 / bn
例子：
2-3 = 1/23 = 1/(2⋅2⋅2) = 1/8 = 0.125
請參閱：負指數