簡約 (5/6)^2e^{-(5/6)}

解

簡約

(\frac{5}{6})^{2} e^{- (\frac{5}{6})}

\frac{25}{36 e ^{\frac{5}{6}}}

十進法表記

0.30180 \dots

解答ステップ

(\frac{5}{6})^{2} e^{- (\frac{5}{6})}

指数の規則を適用する:

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

= (\frac{5}{6})^{2} \frac{1}{e ^{\frac{5}{6}}}

(\frac{5}{6})^{2} = \frac{5 ^{2}}{6 ^{2}}

= \frac{5 ^{2}}{6 ^{2}} \cdot \frac{1}{e ^{\frac{5}{6}}}

分数を乗じる:

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

= \frac{5 ^{2} \cdot 1}{6 ^{2} e ^{\frac{5}{6}}}

乗算:

5^{2} \cdot 1 = 5^{2}

= \frac{5 ^{2}}{6 ^{2} e ^{\frac{5}{6}}}

5^{2} = 25

= \frac{25}{6 ^{2} e ^{\frac{5}{6}}}

6^{2} = 36

= \frac{25}{36 e ^{\frac{5}{6}}}