如何划分指数。
对于同底的指数,我们应该减去指数:
a n / a m = a n-m
例子:
26 / 23 = 26-3 = 23 = 2⋅2⋅2 = 8
当底不同而a和b的指数相同时,我们可以先除a和b:
a n / b n = (a / b) n
例子:
63 / 23 = (6/2)3 = 33 = 3⋅3⋅3 = 27
当底数和指数不同时,我们必须计算每个指数然后除法:
a n / b m
例子:
62 / 33 = 36 / 27 = 1.333
对于同底的指数,我们可以减去指数:
a-n / a-m = a-n-(-m) = am-n
例子:
2-3 / 2-5 = 25-3 = 22 = 2⋅2 = 4
当底数不同而a和b的指数相同时,我们可以先将a和b相乘:
a-n / b-n = (a/b)-n = 1 / (a/b)n = (b/a)n
例子:
3-2 / 4-2 = (4/3)2 = 1.7778
当底数和指数不同时,我们必须计算每个指数然后除法:
a-n / b-m = bm / an
例子:
3-2 / 4-3 = 43 / 32 = 64 / 9 = 7.111
用相同分数底的指数除分数:
(a / b)n / (a / b)m = (a / b)n-m
例子:
(4/3)3 / (4/3)2 = (4/3)3-2 = (4/3)1 = 4/3 = 1.333
用相同指数的指数除分数:
(a / b)n / (c / d)n = ((a / b)/(c / d))n = ((a⋅d / b⋅c))n
例子:
(4/3)3 / (3/5)3 = ((4/3)/(3/5))3 = ((4⋅5)/(3⋅3))3 = (20/9)3 = 10.97
用不同底数和指数的指数除分数:
(a / b) n / (c / d) m
(4/3)3 / (1/2)2 = 2.37 / 0.25 = 9.481
用相同的分数指数除以分数指数:
a n/m / b n/m = (a / b) n/m
例子:
33/2 / 23/2 = (3/2)3/2 = 1.53/2 = √(1.53) = √3.375 = 1.837
同底分数指数相除:
a n/m / a k/j = a (n/m)-(k/j)
例子:
23/2 / 24/3 = 2(3/2)-(4/3) = 2(1/6) = 6√2 = 1.122
将分数指数与不同的指数和分数相除:
a n/m / b k/j
23/2 / 24/3 = √(23) / 3√(24) = 2.828 / 2.52 = 1.1222
对于同底的指数,我们可以减去指数:
xn / xm = xn-m
例子:
x5 / x3 = (x⋅x⋅x⋅x⋅x) / (x⋅x⋅x) = x5-3 = x2