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

The solution to e^{-2x}\times (-e^{-x}) is -1/(e^{3x)}

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

simplify

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

- \frac{1}{e ^{3 x}}

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

= - \frac{1}{e ^{3 x}}

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What is e^{-2x}\times (-e^{-x}) ?
The solution to e^{-2x}\times (-e^{-x}) is -1/(e^{3x)}