指数の規則、指数の法則、および例。
a の n 乗は、a の n 回の乗算に等しくなります。
a n = a × a × ... × a
n回
a は底、n は指数です。
31 = 3
32 = 3 × 3 = 9
33 = 3 × 3 × 3 = 27
34 = 3 × 3 × 3 × 3 = 81
35 = 3 × 3 × 3 × 3 × 3 = 243
ルール名 | ルール | 例 |
---|---|---|
商品のルール | 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 | |
商の規則 | n /am =an -m _ | 2 5 / 2 3 = 2 5-3 = 4 |
a n / b n = ( a / b ) n | 4 3 / 2 3 = (4/2) 3 = 8 | |
パワールール | ( 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 | |
負の指数 | b -n = 1 / bn | 2 -3 = 1/2 3 = 0.125 |
ゼロルール | b 0 = 1 | 5 0 = 1 |
0 n = 0 、n >0の場合 | 0 5 = 0 | |
一つのルール | b 1 = b | 5 1 = 5 |
1 n = 1 | 1 5 = 1 | |
マイナスワンのルール | (-1) 5 = -1 | |
導関数の規則 | ( x n ) ' = n ⋅ x n -1 | ( x 3 ) ' = 3⋅ x 3-1 |
積分則 | ∫ x n dx = x n +1 /( n +1)+ C | ∫ × 2 dx = × 2+1 /(2+1)+ C |
an ⋅ am = an+m
例:
23 ⋅ 24 = 23+4 = 27 = 2⋅2⋅2⋅2⋅2⋅2⋅2 = 128
an ⋅ bn = (a ⋅ b)n
例:
32 ⋅ 42 = (3⋅4)2 = 122 = 12⋅12 = 144
参照:指数の乗算
an / am = an-m
例:
25 / 23 = 25-3 = 22 = 2⋅2 = 4
an / bn = (a / b)n
例:
43 / 23 = (4/2)3 = 23 = 2⋅2⋅2 = 8
参照:指数の除算
(an) m = a n⋅m
例:
(23)2 = 23⋅2 = 26 = 2⋅2⋅2⋅2⋅2⋅2 = 64
a nm = a (nm)
例:
232 = 2(32) = 2(3⋅3) = 29 = 2⋅2⋅2⋅2⋅2⋅2⋅2⋅2⋅2 = 512
m√(a n) = a n/m
例:
2√(26) = 26/2 = 23 = 2⋅2⋅2 = 8
b-n = 1 / bn
例:
2-3 = 1/23 = 1/(2⋅2⋅2) = 1/8 = 0.125
参照:負の指数