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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

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

f (t) = e^{- 6 l n (t)}

e^{- x^{2}}

\frac{d}{d t} ((x (t, P (x, t))) P (x, t) t^{2} e^{- 3 t})

- e^{- 0}

f (x) = - 3 x e^{- 3 x}

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