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

The solution to e^{(-x^2)/2}*e^{(-x^2)/2} is e^{-x^2}

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

simplify

e^{\frac{- x ^{2}}{2}} \cdot e^{\frac{- x ^{2}}{2}}

e^{- x^{2}}

Solution steps

e^{\frac{- x ^{2}}{2}} e^{\frac{- x ^{2}}{2}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{\frac{- x ^{2}}{2}} e^{\frac{- x ^{2}}{2}} = e^{\frac{- x ^{2}}{2} + \frac{- x ^{2}}{2}}

= e^{\frac{- x ^{2}}{2} + \frac{- x ^{2}}{2}}

Combine the fractions

\frac{- x ^{2}}{2} + \frac{- x ^{2}}{2} : - x^{2}

= e^{- x^{2}}

3.7 e^{4} \cdot 5.2 e^{- 5}

20 \cdot (\frac{0.1}{3})^{- \frac{1.67 - 1}{1.67}}

1 0^{- 5.8} \cdot 17 \cdot 1000

4.28 \cdot 1 0^{- 7} \frac{1}{0.63}

(2 x^{3} y^{4} z^{5}) 11 x^{2} y^{2} z^{2}

What is e^{(-x^2)/2}*e^{(-x^2)/2} ?
The solution to e^{(-x^2)/2}*e^{(-x^2)/2} is e^{-x^2}