What is e^{-st}e^{2t}sin(3t) ?

The solution to e^{-st}e^{2t}sin(3t) is e^{2t-st}sin(3t)

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simplify e^{-st}e^{2t}sin(3t)

simplify

e^{- s t} e^{2 t} sin (3 t)

e^{2 t - s t} sin (3 t)

Solution steps

e^{- s t} e^{2 t} sin (3 t)

Apply exponent rule:

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

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

= e^{- s t + 2 t} sin (3 t)

50 e^{- 2.5}

3 (12.8 \cdot 1 0^{- 6}) (96 - 25)

(4 a^{2}) \cdot (5 a^{3})

56.064 \cdot 1 0^{- 3} \cdot 273

9^{8} \cdot e^{- 9}

What is e^{-st}e^{2t}sin(3t) ?
The solution to e^{-st}e^{2t}sin(3t) is e^{2t-st}sin(3t)