What is e^{-5x}*(-2e^{-2x}) ?

The solution to e^{-5x}*(-2e^{-2x}) is -2/(e^{7x)}

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simplify e^{-5x}*(-2e^{-2x})

simplify

e^{- 5 x} \cdot (- 2 e^{- 2 x})

- \frac{2}{e ^{7 x}}

Solution steps

e^{- 5 x} (- 2 e^{- 2 x})

Apply exponent rule:

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

= \frac{1}{e ^{5 x}} (- 2 e^{- 2 x})

Remove parentheses:

(- a) = - a

= - \frac{1}{e ^{5 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 ^{5 x}}

Multiply the numbers:

1 \cdot 2 = 2

= - \frac{2 e ^{- 2 x}}{e ^{5 x}}

Apply exponent rule:

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

\frac{e ^{- 2 x}}{e ^{5 x}} = e^{- 2 x - 5 x} = e^{- 7 x}

= - \frac{2}{e ^{7 x}}

e^{- 2 y^{2}} \cdot e^{- 3 y^{2}}

1.63 \cdot 1 0^{- 3}

1.3 e^{- 0.3 (x)}

1.8 \cdot 10 e^{- 5}

- x^{2} (3 x - 5)^{2}

What is e^{-5x}*(-2e^{-2x}) ?
The solution to e^{-5x}*(-2e^{-2x}) is -2/(e^{7x)}