What is simplify-e^{-t}*(-e^te^{-2t}) ?

The solution to simplify-e^{-t}*(-e^te^{-2t}) is 1/(e^{2t)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify-e^{-t}*(-e^te^{-2t})

simplify

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

\frac{1}{e ^{2 t}}

Solution steps

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

Apply exponent rule:

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

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

Apply rule

- (- a) = a

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

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

e^{t} e^{- 2 t} = e^{t - 2 t}

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

Add similar elements:

t - 2 t = - t

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

Multiply fractions:

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

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

Multiply:

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

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

Apply exponent rule:

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

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

= \frac{1}{e ^{2 t}}

(49.49747) (7.78572 \cdot 1 0^{- 11}) (0.5)

(1.42 \cdot 1 0^{- 5}) \cdot \frac{8740}{1.42}

64

e^{- \frac{10}{24}}

8.5 \cdot 1 0^{- 3} \cdot 10

What is simplify-e^{-t}*(-e^te^{-2t}) ?
The solution to simplify-e^{-t}*(-e^te^{-2t}) is 1/(e^{2t)}