What is 1/3 (e^{3t}-1)^2e^{-5t} ?

The solution to 1/3 (e^{3t}-1)^2e^{-5t} is ((e^{3t}-1)^2)/(3e^{5t)}

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simplify 1/3 (e^{3t}-1)^2e^{-5t}

simplify

\frac{1}{3} (e^{3 t} - 1)^{2} e^{- 5 t}

\frac{( e ^{3 t} - 1 ) ^{2}}{3 e ^{5 t}}

Solution steps

\frac{1}{3} (e^{3 t} - 1)^{2} e^{- 5 t}

Apply exponent rule:

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

= \frac{1}{3} \cdot \frac{1}{e ^{5 t}} (e^{3 t} - 1)^{2}

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 ^{3 t} - 1 ) ^{2}}{3 e ^{5 t}}

Multiply:

1 \cdot 1 \cdot (e^{3 t} - 1)^{2} = (e^{3 t} - 1)^{2}

= \frac{( e ^{3 t} - 1 ) ^{2}}{3 e ^{5 t}}

e^{- 0.15 \frac{1}{4}}

e^{(- 4 x)}

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

(x + 1)^{2} (x + 4)^{2}

What is 1/3 (e^{3t}-1)^2e^{-5t} ?
The solution to 1/3 (e^{3t}-1)^2e^{-5t} is ((e^{3t}-1)^2)/(3e^{5t)}