What is (0.5^2)/(2!)e^{-0.5} ?

The solution to (0.5^2)/(2!)e^{-0.5} is 0.07581…

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simplify (0.5^2)/(2!)e^{-0.5}

simplify

\frac{0. 5 ^{2}}{2 !} e^{- 0.5}

0.07581 \dots

Solution steps

\frac{0. 5 ^{2}}{2 !} e^{- 0.5}

Apply exponent rule:

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

= \frac{0. 5 ^{2}}{2 !} \cdot \frac{1}{e}

Multiply fractions:

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

= \frac{0. 5 ^{2} \cdot 1}{2 ! e}

Multiply:

0. 5^{2} \cdot 1 = 0. 5^{2}

= \frac{0. 5 ^{2}}{e \cdot 2 !}

0. 5^{2} = 0.25

= \frac{0.25}{e \cdot 2 !}

2! e = 2 e

= \frac{0.25}{2 e}

e = 1.64872 \dots

= \frac{0.25}{2 \cdot 1.64872 \dots}

Multiply the numbers:

2 \cdot 1.64872 \dots = 3.29744 \dots

= \frac{0.25}{3.29744 \dots}

Divide the numbers:

\frac{0.25}{3.29744 \dots} = 0.07581 \dots

= 0.07581 \dots

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