What is l^{-1}2te^{-2t} ?

The solution to l^{-1}2te^{-2t} is (2t)/(le^{2t)}

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simplify l^{-1}2te^{-2t}

simplify

l^{- 1} 2 t e^{- 2 t}

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

Solution steps

l^{- 1} \cdot 2 t e^{- 2 t}

Apply exponent rule:

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

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

Apply exponent rule:

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

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 1 \cdot 2 = 2

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

2.127659574 \cdot 1 0^{- 4}

e^{- 4.198}

3.59 \cdot 1 0^{- 3}

\frac{9}{0.0095} \cdot 1 0^{- 6}

(e^{t})^{\frac{1}{20}}