簡約-2.179*10^{-18}(1/(7^2)-1/(3^2))

解

簡約

- 2.179 \cdot 1 0^{- 18} (\frac{1}{7 ^{2}} - \frac{1}{3 ^{2}})

\frac{2179}{11025 \cdot 1 0 ^{18}}

十進法表記

1.97642 E - 19

解答ステップ

- 2.179 \cdot 1 0^{- 18} (\frac{1}{7 ^{2}} - \frac{1}{3 ^{2}})

指数の規則を適用する:

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

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

= - 2.179 \cdot \frac{1}{1 0 ^{18}} (\frac{1}{7 ^{2}} - \frac{1}{3 ^{2}})

\frac{1}{7 ^{2}} - \frac{1}{3 ^{2}} = - \frac{40}{441}

= - 2.179 \cdot \frac{1}{1 0 ^{18}} (- \frac{40}{441})

規則を適用する:

- a (- b) = ab

- 2.179 \cdot \frac{1}{1 0 ^{18}} (- \frac{40}{441}) = 2.179 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{40}{441}

= 2.179 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{40}{441}

2.179 = \frac{2179}{1000}

= \frac{2179}{1000} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{40}{441}

\frac{2179}{1000} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{40}{441} = \frac{2179}{11025 \cdot 1 0 ^{18}}

= \frac{2179}{11025 \cdot 1 0 ^{18}}