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

The solution to 3e^{-2t}(-e^{-st}) is -3e^{-ts-2t}

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simplify 3e^{-2t}(-e^{-st})

simplify

3 e^{- 2 t} (- e^{- s t})

- 3 e^{- t s - 2 t}

Solution steps

3 e^{- 2 t} (- e^{- s t})

Apply exponent rule:

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

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

Remove parentheses:

(- a) = - a

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

Multiply fractions:

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

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

Multiply the numbers:

1 \cdot 3 = 3

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

Apply exponent rule:

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

\frac{e ^{- t s}}{e ^{2 t}} = e^{- t s - 2 t}

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

(9 n^{2}) (m - 1)^{2}

1 0^{- 4} \cdot 1.489

e^{y} e^{l n (2 x)}

(0.4529) \cdot (1.142 x 1 0^{- 4})

x^{- 1} (ln (x))