What is e^{-x^2-2x}*e^{2x} ?

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

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simplify e^{-x^2-2x}*e^{2x}

simplify

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

e^{- x^{2}}

Solution steps

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

Apply exponent rule:

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

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

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

Add similar elements:

- 2 x + 2 x = 0

= e^{- x^{2}}

6.022 \cdot (1 0^{2})^{3} \cdot 2

20000 (1.024)^{- 80}

e^{- 1 \cdot 200}

2 x - x (x)