化简-2.179*10^{-18}(1/(4^2)-1/(9^2))

解答

化简

- 2.179 \cdot 1 0^{- 18} (\frac{1}{4 ^{2}} - \frac{1}{9 ^{2}})

- \frac{28327}{259200 \cdot 1 0 ^{18}}

十进制

0

求解步骤

- 2.179 \cdot 1 0^{- 18} (\frac{1}{4 ^{2}} - \frac{1}{9 ^{2}})

使用指数法则:

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

1 0^{- 18} = \frac{1}{1 0 ^{18}}

= - 2.179 \cdot \frac{1}{1 0 ^{18}} (\frac{1}{4 ^{2}} - \frac{1}{9 ^{2}})

\frac{1}{4 ^{2}} - \frac{1}{9 ^{2}} = \frac{65}{1296}

= - 2.179 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{65}{1296}

2.179 = \frac{2179}{1000}

= - \frac{2179}{1000} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{65}{1296}

- \frac{2179}{1000} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{65}{1296} = - \frac{28327}{259200 \cdot 1 0 ^{18}}

= - \frac{28327}{259200 \cdot 1 0 ^{18}}

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