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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

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

6.3 \cdot 1 0^{- 6}

6.3 \cdot 1 0^{- 2}

(y^{'} (t) + y)^{2} (L - y^{'} (t) - y)^{2}

x^{2} + y^{2} \cdot 16 - x^{2} - y^{2}

(3 x^{\frac{1}{3}}) (4 x^{\frac{1}{6}})

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