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

The solution to e^{-x}(-5e^{-5x}) is -5/(e^{6x)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

simplify

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

- \frac{5}{e ^{6 x}}

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 5 = 5

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

Apply exponent rule:

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

\frac{e ^{- 5 x}}{e ^{x}} = e^{- 5 x - x} = e^{- 6 x}

= - \frac{5}{e ^{6 x}}

(2 x^{8}) (4 x^{4})

e^{- 0.05085}

e^{- 144}

e^{4} \cdot e

7.81 \cdot 1 0^{- 5}