化简 [ 1/(0.011)+(0.7722)/(0.0181)]^{-1}*1.6

解答

化简

[\frac{1}{0.011} + \frac{0.7722}{0.0181}]^{- 1} \cdot 1.6

\frac{7964}{664855}

十进制

0.01197 \dots

求解步骤

(\frac{1}{0.011} + \frac{0.7722}{0.0181})^{- 1} \cdot 1.6

使用指数法则:

a^{- 1} = \frac{1}{a}

(\frac{1}{0.011} + \frac{0.7722}{0.0181})^{- 1} = \frac{1}{\frac{1}{0.011} + \frac{0.7722}{0.0181}}

= \frac{1}{\frac{1}{0.011} + \frac{0.7722}{0.0181}} \cdot 1.6

\frac{1}{\frac{1}{0.011} + \frac{0.7722}{0.0181}} = \frac{3.96408 E - 8}{\frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181}}

= \frac{3.96408 E - 8}{\frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181}} \cdot 1.6

\frac{3.96408 E - 8}{\frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181}} = \frac{3964081}{1.0 E 14 ( \frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181} )}

= \frac{3964081}{1.0 E 14 ( \frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181} )} \cdot 1.6

\frac{3.96408 E - 8}{0.011} + \frac{3.06106 E - 8}{0.0181} = \frac{360371}{100000000000} + \frac{84559761}{5.0 E 13}

= \frac{3964081}{1.0 E 14 ( \frac{360371}{100000000000} + \frac{84559761}{5.0 E 13} )} \cdot 1.6

消掉

\frac{3964081}{1.0 E 14 ( \frac{360371}{100000000000} + \frac{84559761}{5.0 E 13} )} : \frac{1991}{265942}

= \frac{1991}{265942} \cdot 1.6

1.6 = \frac{8}{5}

= \frac{1991}{265942} \cdot \frac{8}{5}

\frac{1991}{265942} \cdot \frac{8}{5} = \frac{7964}{664855}

= \frac{7964}{664855}

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