簡約 e^{-1/(0.75)}*(1-e^{-1/(0.75)})^4

解

簡約

e^{- \frac{1}{0.75}} \cdot (1 - e^{- \frac{1}{0.75}})^{4}

0.07751 \dots

解答ステップ

e^{- \frac{1}{0.75}} (1 - e^{- \frac{1}{0.75}})^{4}

指数の規則を適用する:

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

= \frac{1}{e ^{\frac{1}{0.75}}} (- e^{- \frac{1}{0.75}} + 1)^{4}

(1 - e^{- \frac{1}{0.75}})^{4} = 0.73640 \dots^{4}

= 0.73640 \dots^{4} \cdot \frac{1}{e ^{\frac{1}{0.75}}}

分数を乗じる:

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

= \frac{1 \cdot 0.73640 \dots ^{4}}{e ^{\frac{1}{0.75}}}

乗算:

1 \cdot 0.73640 \dots^{4} = 0.73640 \dots^{4}

= \frac{0.73640 \dots ^{4}}{e ^{\frac{1}{0.75}}}

0.73640 \dots^{4} = 0.29407 \dots

= \frac{0.29407 \dots}{e ^{\frac{1}{0.75}}}

e^{\frac{1}{0.75}} = 3.79366 \dots

= \frac{0.29407 \dots}{3.79366 \dots}

数を割る:

\frac{0.29407 \dots}{3.79366 \dots} = 0.07751 \dots

= 0.07751 \dots