簡約-2.18*10^{-18}(1/(5^2)-1/(4^2))

解

簡約

- 2.18 \cdot 1 0^{- 18} (\frac{1}{5 ^{2}} - \frac{1}{4 ^{2}})

\frac{981}{1 0 ^{18} \cdot 20000}

十進法表記

4.905 E - 20

解答ステップ

- 2.18 \cdot 1 0^{- 18} (\frac{1}{5 ^{2}} - \frac{1}{4 ^{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}}

= - 2.18 \cdot \frac{1}{1 0 ^{18}} (\frac{1}{5 ^{2}} - \frac{1}{4 ^{2}})

\frac{1}{5 ^{2}} - \frac{1}{4 ^{2}} = - \frac{9}{400}

= - 2.18 \cdot \frac{1}{1 0 ^{18}} (- \frac{9}{400})

規則を適用する:

- a (- b) = ab

- 2.18 \cdot \frac{1}{1 0 ^{18}} (- \frac{9}{400}) = 2.18 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{9}{400}

= 2.18 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{9}{400}

2.18 = \frac{109}{50}

= \frac{109}{50} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{9}{400}

\frac{109}{50} \cdot \frac{1}{1 0 ^{18}} \cdot \frac{9}{400} = \frac{981}{1 0 ^{18} \cdot 20000}

= \frac{981}{1 0 ^{18} \cdot 20000}