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

103 \cdot 10

4.8 \cdot 1 0^{- 7}

sin (x) (sin^{2} (x))

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

\frac{2}{\frac{2}{25}}