What is e^{-x^2}\times e^{x^2} ?

The solution to e^{-x^2}\times e^{x^2} is 1

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simplify e^{-x^2}\times e^{x^2}

simplify

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

1

Solution steps

e^{- x^{2}} e^{x^{2}}

Apply exponent rule:

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

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

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

Add similar elements:

- x^{2} + x^{2} = 0

= e^{0}

Apply rule

a^{0} = 1, a \neq = 0

= 1

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