展开 (6(7^{20}-5^{20}))/(7^{20)}-144/49

解答

展开

\frac{6 ( 7 ^{20} - 5 ^{20} )}{7 ^{20}} - \frac{144}{49}

6 - \frac{5 ^{20} \cdot 6}{7 ^{20}} - \frac{144}{49}

十进制

3.05405 \dots

求解步骤

\frac{6 ( 7 ^{20} - 5 ^{20} )}{7 ^{20}} - \frac{144}{49}

乘开

6 (7^{20} - 5^{20}) : 7^{20} \cdot 6 - 5^{20} \cdot 6

= \frac{7 ^{20} \cdot 6 - 5 ^{20} \cdot 6}{7 ^{20}} - \frac{144}{49}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{7 ^{20} \cdot 6 - 5 ^{20} \cdot 6}{7 ^{20}} = \frac{7 ^{20} \cdot 6}{7 ^{20}} - \frac{5 ^{20} \cdot 6}{7 ^{20}}

= \frac{7 ^{20} \cdot 6}{7 ^{20}} - \frac{5 ^{20} \cdot 6}{7 ^{20}} - \frac{144}{49}

消掉

\frac{7 ^{20} \cdot 6}{7 ^{20}} : 6

= 6 - \frac{5 ^{20} \cdot 6}{7 ^{20}} - \frac{144}{49}

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