What is expand e^{1/3 ((s^2)/2-9ln|s|)} ?

The solution to expand e^{1/3 ((s^2)/2-9ln|s|)} is (e^{(s^2)/6})/(|s|^3)

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expand e^{1/3 ((s^2)/2-9ln|s|)}

expand

e^{\frac{1}{3} (\frac{s ^{2}}{2} - 9 l n ∣ s ∣)}

\frac{e ^{\frac{s ^{2}}{6}}}{∣ s ∣ ^{3}}

Solution steps

e^{\frac{1}{3} (\frac{s ^{2}}{2} - 9 l n ∣ s ∣)}

Expand

\frac{1}{3} (\frac{s ^{2}}{2} - 9 ln ∣ s ∣) : \frac{s ^{2}}{6} - 3 ln ∣ s ∣

= e^{\frac{s ^{2}}{6} - 3 l n ∣ s ∣}

Simplify

= \frac{1}{6} s^{2}

= e^{\frac{1}{6} s^{2} - 3 l n ∣ s ∣}

Apply exponent rule:

a^{b + c} = a^{b} a^{c}

= e^{- 3 l n ∣ s ∣} e^{\frac{1}{6} s^{2}}

Simplify

e^{- 3 l n ∣ s ∣} : ∣ s ∣^{- 3}

= ∣ s ∣^{- 3} e^{\frac{1}{6} s^{2}}

e^{\frac{1}{6} s^{2}} = e^{\frac{s ^{2}}{6}}

= e^{\frac{s ^{2}}{6}} ∣ s ∣^{- 3}

Apply exponent rule:

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

∣ s ∣^{- 3} = \frac{1}{∣ s ∣ ^{3}}

= e^{\frac{s ^{2}}{6}} \frac{1}{∣ s ∣ ^{3}}

Multiply fractions:

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

= \frac{1 \cdot e ^{\frac{s ^{2}}{6}}}{∣ s ∣ ^{3}}

Multiply:

1 \cdot e^{\frac{s ^{2}}{6}} = e^{\frac{s ^{2}}{6}}

= \frac{e ^{\frac{s ^{2}}{6}}}{∣ s ∣ ^{3}}

2.8 tan (0.7 x - 1.8) - 2 (- 2, - 0.53)

\frac{x}{( x ^{2} - 2 x + 2 ) ( x ^{2} + 1 )}

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\frac{2 ( 6 + 3 )}{11}

1 + \frac{k ( s + 4 )}{s ( s + 0.5 ) ( s + 1 ) ( s ^{2} + 0.4 s + 4 )}

What is expand e^{1/3 ((s^2)/2-9ln|s|)} ?
The solution to expand e^{1/3 ((s^2)/2-9ln|s|)} is (e^{(s^2)/6})/(|s|^3)