What is (2pi)^{-0.5}e^{(-((3.95)^2)/2)} ?

The solution to (2pi)^{-0.5}e^{(-((3.95)^2)/2)} is 0.00016…

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simplify (2pi)^{-0.5}e^{(-((3.95)^2)/2)}

simplify

(2 π)^{- 0.5} e^{(- \frac{( 3.95 ) ^{2}}{2})}

0.00016 \dots

Solution steps

(2 π)^{- 0.5} e^{(- \frac{( 3.95 ) ^{2}}{2})}

Apply exponent rule:

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

= e^{- \frac{3.9 5 ^{2}}{2}} \frac{1}{( 2 π ) ^{0.5}}

Apply exponent rule:

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

= \frac{1}{( 2 π ) ^{0.5}} \cdot \frac{1}{e ^{\frac{3.9 5 ^{2}}{2}}}

\frac{1}{( 2 π ) ^{0.5}} = \frac{1}{2 ^{0.5} π ^{0.5}}

= \frac{1}{2 ^{0.5} π ^{0.5}} \cdot \frac{1}{e ^{\frac{3.9 5 ^{2}}{2}}}

Multiply fractions:

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

= \frac{1 \cdot 1}{2 ^{0.5} π ^{0.5} e ^{\frac{3.9 5 ^{2}}{2}}}

Multiply the numbers:

1 \cdot 1 = 1

= \frac{1}{2 ^{0.5} π ^{0.5} e ^{\frac{3.9 5 ^{2}}{2}}}

3.9 5^{2} = 15.6025

= \frac{1}{2 ^{0.5} π ^{0.5} e ^{\frac{15.6025}{2}}}

2^{0.5} = 1.41421 \dots

= \frac{1}{1.41421 \dots π ^{0.5} e ^{\frac{15.6025}{2}}}

π^{0.5} = 1.77245 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots e ^{\frac{15.6025}{2}}}

e^{\frac{15.6025}{2}} = 2443.65463 \dots

= \frac{1}{1.41421 \dots \cdot 1.77245 \dots \cdot 2443.65463 \dots}

Multiply the numbers:

1.41421 \dots \cdot 1.77245 \dots \cdot 2443.65463 \dots = 6125.33380 \dots

= \frac{1}{6125.33380 \dots}

Divide the numbers:

\frac{1}{6125.33380 \dots} = 0.00016 \dots

= 0.00016 \dots

89.9 e^{- 0, 5 (2)}

- 4.8 \cdot 10 C^{- 19}

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a^{4 n}

(8 x z^{2}) (4 b z - 8 x y^{2} - 8 a z + 8 x z + 2 y + 2 x yz)^{2}

What is (2pi)^{-0.5}e^{(-((3.95)^2)/2)} ?
The solution to (2pi)^{-0.5}e^{(-((3.95)^2)/2)} is 0.00016…