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

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

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

simplify

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

0.07581 \dots

Solution steps

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

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

Multiply:

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

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

0. 5^{2} = 0.25

= \frac{0.25}{2 e}

e = 1.64872 \dots

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

Multiply the numbers:

1.64872 \dots \cdot 2 = 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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