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

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

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

simplify

(2 e^{x}) (- e^{- x}) (e^{x})

- 2 e^{x}

Solution steps

(2 e^{x}) (- e^{- x}) (e^{x})

Apply exponent rule:

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

e^{x} e^{x} = e^{x + x}

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

Add similar elements:

x + x = 2 x

= 2 (- e^{- x}) e^{2 x}

Remove parentheses:

(- a) = - a

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

Apply exponent rule:

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

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

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

Add similar elements:

- x + 2 x = x

= - 2 e^{x}

- 2 e^{- y} d y

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(3 \cdot 1 0^{- 3}) (0.4)