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

The solution to (e^{-x})(-2e^{-2x}) is -2/(e^{3x)}

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

simplify

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

- \frac{2}{e ^{3 x}}

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{e ^{x}} (- 2 e^{- 2 x})

Remove parentheses:

(- a) = - a

= - \frac{1}{e ^{x}} \cdot 2 e^{- 2 x}

Multiply fractions:

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

= - \frac{1 \cdot 2 e ^{- 2 x}}{e ^{x}}

Multiply the numbers:

1 \cdot 2 = 2

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = x^{a - b}

\frac{e ^{- 2 x}}{e ^{x}} = e^{- 2 x - x} = e^{- 3 x}

= - \frac{2}{e ^{3 x}}

\frac{( - 2 ) ^{n}}{2 ^{n}}

(2 - 5) (2 - 5)

275 e^{- 0.65}

100

What is (e^{-x})(-2e^{-2x}) ?
The solution to (e^{-x})(-2e^{-2x}) is -2/(e^{3x)}