簡約 (e^{-664.6976300000000…})((e^{0.3411000000000…})^{1971})

解

簡約

(e^{- 664.6976300000000 \dots}) ((e^{0.3411000000000 \dots})^{1971})

2019.22691 \dots

解答ステップ

(e^{- 664.69763 \dots}) ((e^{0.34110 \dots})^{1971})

指数の規則を適用する:

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

= \frac{1}{e ^{664.69763 \dots}} (e^{0.34110 \dots})^{1971}

(e^{0.34110 \dots})^{1971} : e^{672.3081}

= \frac{1}{e ^{664.69763 \dots}} e^{672.3081}

分数を乗じる:

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

= \frac{1 \cdot e ^{672.3081}}{e ^{664.69763 \dots}}

乗算:

1 \cdot e^{672.3081} = e^{672.3081}

= \frac{e ^{672.3081}}{e ^{664.69763 \dots}}

指数の規則を適用する:

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

\frac{e ^{672.3081}}{e ^{664.69763 \dots}} = e^{672.3081 - 664.69763 \dots}

= e^{672.3081 - 664.69763 \dots}

数を引く:

672.3081 - 664.69763 \dots = 7.61047

= e^{7.61047}

e^{7.61047} = 2019.22691 \dots

= 2019.22691 \dots