What is e^{-3s}(2/(s^3)-7/(s^2)+9/s) ?

The solution to e^{-3s}(2/(s^3)-7/(s^2)+9/s) is (9s^2-7s+2)/(e^{3s)s^3}

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simplify e^{-3s}(2/(s^3)-7/(s^2)+9/s)

simplify

e^{- 3 s} (\frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s})

\frac{9 s ^{2} - 7 s + 2}{e ^{3 s} s ^{3}}

Solution steps

e^{- 3 s} (\frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s})

Apply exponent rule:

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

= \frac{1}{e ^{3 s}} (\frac{2}{s ^{3}} + \frac{9}{s} - \frac{7}{s ^{2}})

Multiply fractions:

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

= \frac{1 \cdot ( \frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s} )}{e ^{3 s}}

1 \cdot (\frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s}) = \frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s}

= \frac{\frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s}}{e ^{3 s}}

Join

\frac{2}{s ^{3}} - \frac{7}{s ^{2}} + \frac{9}{s} : \frac{2 - 7 s + 9 s ^{2}}{s ^{3}}

= \frac{\frac{2 - 7 s + 9 s ^{2}}{s ^{3}}}{e ^{3 s}}

Apply the fraction rule:

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

= \frac{2 - 7 s + 9 s ^{2}}{s ^{3} e ^{3 s}}

5^{5} \cdot 3^{5}

e (\frac{7}{2})^{- 2}

(e^{\frac{x}{2}} \cdot cos (2 x)) \cdot (e^{\frac{x}{2}} \cdot cos (x))

e^{- (- 7)^{2}}

e^{x} \cdot \frac{1}{3} e^{- x} x ln (x)

What is e^{-3s}(2/(s^3)-7/(s^2)+9/s) ?
The solution to e^{-3s}(2/(s^3)-7/(s^2)+9/s) is (9s^2-7s+2)/(e^{3s)s^3}