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}}

e^{- 2 x} d x

(e^{- 1})^{2}

6 e^{- 1}

e^{- 30}