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

The solution to e^{-2t}(e^{-2t}-2te^{-2t}) is (-2t+1)/(e^{4t)}

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

simplify

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

\frac{- 2 t + 1}{e ^{4 t}}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

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

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

Factor out common term

e^{- 2 t}

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

Cancel

\frac{e ^{- 2 t} ( 1 - 2 t )}{e ^{2 t}} : \frac{1 - 2 t}{e ^{4 t}}

= \frac{1 - 2 t}{e ^{4 t}}

= \frac{- 2 t + 1}{e ^{4 t}}

100 \cdot e^{- 403.932}

101.32 5^{- \frac{9.81}{( 287 ) ( 276 )} \cdot 3624}

4 \cdot π \cdot 69634000 0^{2} \cdot 5678 \cdot 1 0^{- 8}

What is e^{-2t}(e^{-2t}-2te^{-2t}) ?
The solution to e^{-2t}(e^{-2t}-2te^{-2t}) is (-2t+1)/(e^{4t)}