What is e^{(-365*2/600)}((365*2/600)^3)/(3!) ?

The solution to e^{(-365*2/600)}((365*2/600)^3)/(3!) is (389017)/(1296000e^{73/60)}

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simplify e^{(-3652/600)}((3652/600)^3)/(3!)

simplify

e^{(- 365 \cdot \frac{2}{600})} \frac{( 365 \cdot \frac{2}{600} ) ^{3}}{3 !}

\frac{389017}{1296000 e ^{\frac{73}{60}}}

Decimal Notation

0.08891 \dots

Solution steps

e^{(- 365 \cdot \frac{2}{600})} \frac{( 365 \cdot \frac{2}{600} ) ^{3}}{3 !}

Apply exponent rule:

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

= \frac{1}{e ^{365 \cdot \frac{2}{600}}} \cdot \frac{( 365 \cdot \frac{2}{600} ) ^{3}}{3 !}

\frac{1}{e ^{365 \cdot \frac{2}{600}}} = \frac{1}{e ^{\frac{73}{60}}}

= \frac{1}{e ^{\frac{73}{60}}} \cdot \frac{( 365 \cdot \frac{2}{600} ) ^{3}}{3 !}

\frac{( 365 \cdot \frac{2}{600} ) ^{3}}{3 !} = \frac{7 3 ^{3}}{6 0 ^{3} \cdot 3 !}

= \frac{7 3 ^{3}}{6 0 ^{3} \cdot 3 !} \cdot \frac{1}{e ^{\frac{73}{60}}}

Multiply fractions:

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

= \frac{1 \cdot 7 3 ^{3}}{e ^{\frac{73}{60}} \cdot 6 0 ^{3} \cdot 3 !}

Multiply:

1 \cdot 7 3^{3} = 7 3^{3}

= \frac{7 3 ^{3}}{6 0 ^{3} e ^{\frac{73}{60}} \cdot 3 !}

7 3^{3} = 389017

= \frac{389017}{6 0 ^{3} e ^{\frac{73}{60}} \cdot 3 !}

e^{\frac{73}{60}} \cdot 6 0^{3} \cdot 3! = 1296000 e^{\frac{73}{60}}

= \frac{389017}{1296000 e ^{\frac{73}{60}}}

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What is e^{(-365*2/600)}((365*2/600)^3)/(3!) ?
The solution to e^{(-365*2/600)}((365*2/600)^3)/(3!) is (389017)/(1296000e^{73/60)}