簡約 10/100 e^{-(100)/(0.003333)*0.0001}

解

簡約

\frac{10}{100} e^{- \frac{100}{0.003333} \cdot 0.0001}

0.00497 \dots

解答ステップ

\frac{10}{100} e^{- \frac{100}{0.003333} \cdot 0.0001}

指数の規則を適用する:

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

= \frac{10}{100} \cdot \frac{1}{e ^{0.0001 \cdot \frac{100}{0.003333}}}

\frac{10}{100} = \frac{1}{10}

= \frac{1}{10} \cdot \frac{1}{e ^{0.0001 \cdot \frac{100}{0.003333}}}

\frac{1}{e ^{\frac{100}{0.003333} \cdot 0.0001}} = \frac{1}{e ^{3.00030 \dots}}

= \frac{1}{10} \cdot \frac{1}{e ^{3.00030 \dots}}

分数を乗じる:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{1 \cdot 1}{10 e ^{3.00030 \dots}}

数を乗じる:

1 \cdot 1 = 1

= \frac{1}{10 e ^{3.00030 \dots}}

e^{3.00030 \dots} = 20.09156 \dots

= \frac{1}{10 \cdot 20.09156 \dots}

数を乗じる:

10 \cdot 20.09156 \dots = 200.91564 \dots

= \frac{1}{200.91564 \dots}

数を割る:

\frac{1}{200.91564 \dots} = 0.00497 \dots

= 0.00497 \dots