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受欢迎的代数 >

化简 2.61704*(1/2)^{1000/24100}

解答

化简

2.61704 \cdot (\frac{1}{2})^{\frac{1000}{24100}}

解答

\frac{32713}{12500 \cdot 2 ^{\frac{10}{241}}}

+1

十进制

2.54284 \dots

求解步骤

2.61704 (\frac{1}{2})^{\frac{1000}{24100}}

使用指数法则:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

(\frac{1}{2})^{\frac{1000}{24100}} = \frac{1 ^{\frac{1000}{24100}}}{2 ^{\frac{1000}{24100}}}

= 2.61704 \cdot \frac{1 ^{\frac{1000}{24100}}}{2 ^{\frac{1000}{24100}}}

1^{\frac{1000}{24100}} = 1

= 2.61704 \cdot \frac{1}{2 ^{\frac{1000}{24100}}}

消掉

\frac{1000}{24100} : \frac{10}{241}

= 2.61704 \cdot \frac{1}{2 ^{\frac{10}{241}}}

2.61704 \cdot \frac{1}{2 ^{\frac{10}{241}}} = \frac{2.61704}{2 ^{\frac{10}{241}}}

= \frac{2.61704}{2 ^{\frac{10}{241}}}

\frac{2.61704}{2 ^{\frac{10}{241}}} = \frac{261704}{100000 \cdot 2 ^{\frac{10}{241}}}

= \frac{261704}{100000 \cdot 2 ^{\frac{10}{241}}}

因式分解数字:

261704 = 8 \cdot 32713

= \frac{8 \cdot 32713}{100000 \cdot 2 ^{\frac{10}{241}}}

因式分解数字:

100000 = 8 \cdot 12500

= \frac{8 \cdot 32713}{8 \cdot 12500 \cdot 2 ^{\frac{10}{241}}}

约分:

8

= \frac{32713}{12500 \cdot 2 ^{\frac{10}{241}}}

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