簡約 (40e^{0.05}-40)e^{-0.05}

解

簡約

(40 e^{0.05} - 40) e^{- 0.05}

1.95082 \dots

解答ステップ

(40 e^{0.05} - 40) e^{- 0.05}

指数の規則を適用する:

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

= \frac{1}{e ^{0.05}} (40 e^{0.05} - 40)

分数を乗じる:

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

= \frac{1 \cdot ( 40 e ^{0.05} - 40 )}{e ^{0.05}}

1 \cdot (40 e^{0.05} - 40) = 40 e^{0.05} - 40

= \frac{40 e ^{0.05} - 40}{e ^{0.05}}

40 e^{0.05} = 42.05084 \dots

= \frac{42.05084 \dots - 40}{e ^{0.05}}

数を引く:

42.05084 \dots - 40 = 2.05084 \dots

= \frac{2.05084 \dots}{e ^{0.05}}

e^{0.05} = 1.05127 \dots

= \frac{2.05084 \dots}{1.05127 \dots}

数を割る:

\frac{2.05084 \dots}{1.05127 \dots} = 1.95082 \dots

= 1.95082 \dots