簡約 (pi17.65)/(23.972^{1.8)}e^{(-pi/4 ((17.65)/(3.972))^{1.8})}

解

簡約

\frac{π \cdot 17.65}{2 \cdot 3.97 2 ^{1.8}} e^{(- \frac{π}{4} (\frac{17.65}{3.972})^{1.8})}

0.00002 \dots

解答ステップ

\frac{π 17.65}{2 \cdot 3.97 2 ^{1.8}} e^{(- \frac{π}{4} (\frac{17.65}{3.972})^{1.8})}

指数の規則を適用する:

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

= \frac{17.65 π}{2 \cdot 3.97 2 ^{1.8}} \cdot \frac{1}{e ^{\frac{π}{4} (\frac{17.65}{3.972})^{1.8}}}

\frac{1}{e ^{\frac{π}{4} (\frac{17.65}{3.972})^{1.8}}} = \frac{1}{e ^{11.50836 \dots}}

= \frac{17.65 π}{2 \cdot 3.97 2 ^{1.8}} \cdot \frac{1}{e ^{11.50836 \dots}}

分数を乗じる:

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

= \frac{π 17.65 \cdot 1}{2 \cdot 3.97 2 ^{1.8} e ^{11.50836 \dots}}

数を乗じる:

17.65 \cdot 1 = 17.65

= \frac{17.65 π}{2 \cdot 3.97 2 ^{1.8} e ^{11.50836 \dots}}

3.97 2^{1.8} = 11.97337 \dots

= \frac{17.65 π}{2 \cdot 11.97337 \dots e ^{11.50836 \dots}}

数を乗じる:

17.65 \cdot 3.14159 \dots = 55.44911 \dots

= \frac{55.44911 \dots}{2 \cdot 11.97337 \dots e ^{11.50836 \dots}}

e^{11.50836 \dots} = 99545.25465 \dots

= \frac{55.44911 \dots}{2 \cdot 11.97337 \dots \cdot 99545.25465 \dots}

数を乗じる:

2 \cdot 11.97337 \dots \cdot 99545.25465 \dots = 2383785.58526 \dots

= \frac{55.44911 \dots}{2383785.58526 \dots}

数を割る:

\frac{55.44911 \dots}{2383785.58526 \dots} = 0.00002 \dots

= 0.00002 \dots