化简 1/(0.8)e^{-(1/(0.8)+1)}

解答

化简

\frac{1}{0.8} e^{- (\frac{1}{0.8} + 1)}

0.13174 \dots

求解步骤

\frac{1}{0.8} e^{- (\frac{1}{0.8} + 1)}

使用指数法则:

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

= \frac{1}{0.8} \cdot \frac{1}{e ^{(\frac{1}{0.8} + 1)}}

去除括号:

(a) = a

= \frac{1}{0.8} \cdot \frac{1}{e ^{\frac{1}{0.8} + 1}}

e^{\frac{1}{0.8} + 1} = e^{2.25}

= \frac{1}{0.8} \cdot \frac{1}{e ^{2.25}}

分式相乘:

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

= \frac{1 \cdot 1}{0.8 e ^{2.25}}

数字相乘:

1 \cdot 1 = 1

= \frac{1}{0.8 e ^{2.25}}

e^{2.25} = 9.48773 \dots

= \frac{1}{0.8 \cdot 9.48773 \dots}

数字相乘:

0.8 \cdot 9.48773 \dots = 7.59018 \dots

= \frac{1}{7.59018 \dots}

数字相除:

\frac{1}{7.59018 \dots} = 0.13174 \dots

= 0.13174 \dots

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