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

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

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

simplify

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

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

Solution steps

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

Apply exponent rule:

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

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

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

Multiply:

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

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

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

(4 - x^{2})^{3}

2^{\frac{1}{4}} \cdot 8^{\frac{1}{4}}

0.2 \cdot 1 0^{- 4}

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