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

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

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

simplify

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

\frac{2}{5 e ^{5 t}}

Solution steps

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

Apply exponent rule:

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

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

Multiply fractions:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

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

Multiply the numbers:

1 \cdot 2 = 2

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

Apply exponent rule:

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

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

= \frac{2}{5 e ^{5 t}}

(4 x^{5}) (8 x^{4})

6.64 \cdot 1 0^{- 23}

- e^{(- 2 \cdot 0.5)}

1 \cdot e^{- s t}

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