如何解决分数指数。
底数 b 的 n/m 次方等于:
bn/m = (m√b)n = m√(bn)
例子:
底数 2 的 3/2 次方等于 1 除以底数 2 的 3 次方:
23/2 = 2√(23) = 2.828
带指数的分数:
(a / b)n = an / bn
例子:
(4/3)3 = 43 / 33 = 64 / 27 = 2.37
底数 b 的负 n/m 次方等于 1 除以底数 b 的 n/m 次方:
b-n/m = 1 / bn/m = 1 / (m√b)n
例子:
底数 2 的负 1/2 次方等于 1 除以底数 2 的 1/2 次方:
2-1/2 = 1/21/2 = 1/√2 = 0.7071
底数 a/b 的负 n 次方等于 1 除以底数 a/b 的 n 次方:
(a/b)-n = 1 / (a/b)n = 1 / (an/bn) = bn/an
例子:
底数 2 的负 3 次方等于 1 除以底数 2 的 3 次方:
(2/3)-2 = 1 / (2/3)2 = 1 / (22/32) = 32/22 = 9/4 = 2.25
具有相同分数指数的乘法分数指数:
a n/m ⋅ b n/m = (a ⋅ b) n/m
例子:
23/2 ⋅ 33/2 = (2⋅3)3/2 = 63/2 = √(63) = √216 = 14.7
具有相同底数的乘法分数指数:
a n/m ⋅ a k/j = a (n/m)(k/j)
例子:
23/2 ⋅ 24/3 = 2(3/2)((4/3) = 7.127
具有不同指数和分数的乘法分数指数:
a n/m ⋅ b k/j
例子:
23/2 ⋅ 34/3 = √(23) ⋅ 3√(34) = 2.828 ⋅ 4.327 = 12.237
具有相同分数基数的乘法分数指数:
(a / b)n ⋅ (a / b)m = (a / b)n+m
例子:
(4/3)3 ⋅ (4/3)2 = (4/3)3+2 = (4/3)5 = 45 / 35 = 4.214
具有相同指数的乘法分数指数:
(a / b)n ⋅ (c / d)n = ((a / b)⋅(c / d))n
例子:
(4/3)3 ⋅ (3/5)3 = ((4/3)/(3/5))3 = (4/5)3 = 0.83 = 0.8⋅0.8⋅0.8 = 0.512
具有不同基数和指数的乘法分数指数:
(a / b) n ⋅ (c / d) m
例子:
(4/3)3 ⋅ (1/2)2 = 2.37 ⋅ 0.25 = 0.5925
具有相同分数指数的除法分数指数:
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
具有相同底数的除法分数指数:
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
具有不同指数和分数的除法分数指数:
a n/m / b k/j
例子:
23/2 / 34/3 = √(23) / 3√(34) = 2.828 / 4.327 = 0.654
具有相同分数基数的除法分数指数:
(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
具有相同指数的除法分数指数:
(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
具有不同基数和指数的除法分数指数:
(a / b) n / (c / d) m
例子:
(4/3)3 / (1/2)2 = 2.37 / 0.25 = 9.481
通过首先提高每个指数然后相加来添加分数指数:
an/m + bk/j
例子:
33/2 + 25/2 = √(33) + √(25) = √(27) + √(32) = 5.196 + 5.657 = 10.853
添加相同的基数 b 和指数 n/m:
bn/m + bn/m = 2bn/m
例子:
42/3 + 42/3 = 2⋅42/3 = 2 ⋅ 3√(42) = 5.04
通过首先提高每个指数然后相减来减去分数指数:
an/m - bk/j
例子:
33/2 - 25/2 = √(33) - √(25) = √(27) - √(32) = 5.196 - 5.657 = -0.488
减去相同的基数 b 和指数 n/m:
3bn/m - bn/m = 2bn/m
例子:
3⋅42/3 - 42/3 = 2⋅42/3 = 2 ⋅ 3√(42) = 5.04
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