What is 1/(sqrt(2))e^{-t}*(-e^{2t}) ?

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

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simplify 1/(sqrt(2))e^{-t}*(-e^{2t})

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply:

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

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

Apply exponent rule:

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

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

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

e^{- 0.14 \cdot 4}

3983 \cdot π \cdot 102 \cdot 1 0^{- 3} \cdot \frac{1510}{6000}

12.835 \cdot 1 0^{- 12} \cdot 0.07

- 6572 e^{- 0.3286 \cdot 3}

9.87 \cdot 1 0^{- 7}

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