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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

= e^{- s t - t} sin (t)

(3 x^{2}) (12 x)

e^{- 3 \cdot 4}

- 2 - 8

(a^{2} b c) (a b^{2} c)

e^{x^{2}} \cdot 6 x e^{2 x}

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