What is simplify-ALb^2e^{-bt}(Ae^{-bt}) ?

The solution to simplify-ALb^2e^{-bt}(Ae^{-bt}) is -A^2Lb^2e^{-2bt}

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simplify-ALb^2e^{-bt}(Ae^{-bt})

simplify

- A L b^{2} e^{- b t} (A e^{- b t})

- A^{2} L b^{2} e^{- 2 b t}

Solution steps

- A L b^{2} e^{- b t} (A e^{- b t})

Apply exponent rule:

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

AA = A^{1 + 1}

= - L b^{2} e^{- b t} A^{1 + 1} e^{- b t}

Add the numbers:

1 + 1 = 2

= - L b^{2} e^{- b t} A^{2} e^{- b t}

Apply exponent rule:

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

e^{- b t} e^{- b t} = e^{- b t - b t}

= - L b^{2} A^{2} e^{- b t - b t}

Add similar elements:

- b t - b t = - 2 b t

= - L b^{2} A^{2} e^{- 2 b t}

x (x e^{x})

a^{3} b^{2} c^{3}

f^{- 1} (90)

e^{- 2 (x + y)}

What is simplify-ALb^2e^{-bt}(Ae^{-bt}) ?
The solution to simplify-ALb^2e^{-bt}(Ae^{-bt}) is -A^2Lb^2e^{-2bt}