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While trying to $\text{Plot}\left[\frac{x^{-2/3} e^ { \left(-\frac{x^{2/3}}{2}\right)}}{\sqrt{2 \pi 9}},\{x,-5,5\}\right]$ in mathematica, I was initially wondered (though mathematica's silence was rationale) that it was not plotted for negative values of $x$.

Plot[1/Sqrt[2*Pi*9]*Exp[-(x^(2/3)/2)]*x^(-2/3), {x, -5, 5}]

After spending a day of struggling to understand the reason, I finally understood the problem - complex roots of power terms involved in above equation.

Though, I was interested in real output only (real solutions only), how to plot the above equation (which is even function from real space to real space) in matematica.

I did try, taking the absolute value of the function above but that didn't work either.

What should be easiest way to let the mathematica know that we are only interested in real output only?

Any suggestions please !

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up vote 3 down vote accepted
Plot[1/Sqrt[2*Pi*9]*Exp[-(x^2)^(1/3)/2] (x^(-2))^(1/3), {x, -5, 5}]
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