What is factor ae^{-2t}+be^{-5t} ?

The solution to factor ae^{-2t}+be^{-5t} is e^{-5t}(e^{3t}a+b)

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factor ae^{-2t}+be^{-5t}

factor

a e^{- 2 t} + b e^{- 5 t}

e^{- 5 t} (e^{3 t} a + b)

Solution steps

a e^{- 2 t} + b e^{- 5 t}

Apply exponent rule:

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

e^{- 2 t} = e^{- 5 t} e^{3 t}

= a e^{- 5 t} e^{3 t} + b e^{- 5 t}

Factor out common term

e^{- 5 t}

= e^{- 5 t} (a e^{3 t} + b)

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What is factor ae^{-2t}+be^{-5t} ?
The solution to factor ae^{-2t}+be^{-5t} is e^{-5t}(e^{3t}a+b)