簡約 2.18*10^{-18}(3^2)(1/(4^2)-1/(6^2))

解

簡約

2.18 \cdot 1 0^{- 18} (3^{2}) (\frac{1}{4 ^{2}} - \frac{1}{6 ^{2}})

\frac{109}{1 0 ^{18} \cdot 160}

十進法表記

6.8125 E - 19

解答ステップ

2.18 \cdot 1 0^{- 18} (3^{2}) (\frac{1}{4 ^{2}} - \frac{1}{6 ^{2}})

規則を適用する:

(a) = a

(3^{2}) = 3^{2}

= 2.18 \cdot 1 0^{- 18} \cdot 3^{2} (\frac{1}{4 ^{2}} - \frac{1}{6 ^{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}} \cdot 3^{2} (\frac{1}{4 ^{2}} - \frac{1}{6 ^{2}})

3^{2} = 9

= 2.18 \cdot \frac{1}{1 0 ^{18}} \cdot 9 (\frac{1}{4 ^{2}} - \frac{1}{6 ^{2}})

\frac{1}{4 ^{2}} - \frac{1}{6 ^{2}} = \frac{5}{144}

= 2.18 \cdot \frac{1}{1 0 ^{18}} \cdot 9 \cdot \frac{5}{144}

数を乗じる:

2.18 \cdot 9 = 19.62

= 19.62 \cdot \frac{1}{1 0 ^{18}} \cdot \frac{5}{144}

= \frac{5}{144} \cdot 19.62 \cdot \frac{1}{1 0 ^{18}}

19.62 = \frac{981}{50}

= \frac{5}{144} \cdot \frac{981}{50} \cdot \frac{1}{1 0 ^{18}}

\frac{5}{144} \cdot \frac{981}{50} \cdot \frac{1}{1 0 ^{18}} = \frac{109}{1 0 ^{18} \cdot 160}

= \frac{109}{1 0 ^{18} \cdot 160}