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受欢迎的代数 >

化简 (10^{3/7}*5^{2/7})^7

解答

化简

(1 0^{\frac{3}{7}} \cdot 5^{\frac{2}{7}})^{7}

解答

25000

求解步骤

(1 0^{\frac{3}{7}} \cdot 5^{\frac{2}{7}})^{7}

使用指数法则:

(a \cdot b)^{n} = a^{n} b^{n}

(1 0^{\frac{3}{7}} \cdot 5^{\frac{2}{7}})^{7} = (1 0^{\frac{3}{7}})^{7} (5^{\frac{2}{7}})^{7}

= (1 0^{\frac{3}{7}})^{7} (5^{\frac{2}{7}})^{7}

(1 0^{\frac{3}{7}})^{7} = 1000

= 1000 (5^{\frac{2}{7}})^{7}

使用指数法则:

(a^{b})^{c} = a^{b c}, a \geq 0

(5^{\frac{2}{7}})^{7} = 5^{\frac{2}{7} \cdot 7}

= 1000 \cdot 5^{\frac{2}{7} \cdot 7}

\frac{2}{7} \cdot 7 = 2

= 1000 \cdot 5^{2}

5^{2} = 25

= 1000 \cdot 25

数字相乘:

1000 \cdot 25 = 25000

= 25000

流行的例子

2 u + 9 = 8 u + 21

3 x^{2} + 6 x - 3 = 0

-2(12x+13)<=-5(13x+7)

- 2 (12 x + 13) \leq - 5 (13 x + 7)

4^{2} + 4

化简 sqrt(410)

s im pl i f y 410