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When I do Plot3D[z^(1/3), {z, -10, 10}] in Mathematica, it just outputs the command back to me. There is no plot.

Oddly, Wolfram Alpha displays a plot just fine.

http://www.wolframalpha.com/input/?i=Plot3D[z^%281%2F3%29%2C++[z%2C+-10%2C+10]]

Is there something different that I have to do in Mathematica?

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    $\begingroup$ 1) A Plot3D needs two dimensions, try Plot. 2) You're going to end up with complex numbers so you'll probably need to specify Re[z^(1/3)] or Im[z^(1/3)], or you'll wind up with inexplicably empty regions. To get the plots you're seeing in Alpha do Plot3D[Re[z^(1/3),{z,-10,10},{x,-10,10}] or Plot3D[Im[z^(1/3),{z,-10,10},{x,-10,10}] $\endgroup$
    – N.J.Evans
    Commented Oct 15, 2015 at 15:21
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    $\begingroup$ Try Plot3D[Re@(z^(1/3)), {z, -10, 10}, {y, -10, 10}] Plot3D[Im@(z^(1/3)), {z, -10, 10}, {y, -10, 10}] $\endgroup$
    – Dimitris
    Commented Oct 15, 2015 at 15:23
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    $\begingroup$ In addition to using Plot instead of Plot3D, you will probably want to use CubeRoot[z] instead of z^(1/3). The former uses the surd form (suitable for getting real values on negative input) whereas the latter uses the principal root. $\endgroup$ Commented Oct 15, 2015 at 15:29
  • $\begingroup$ @DanielLichtblau: Well, not if $z$ is a complex number. $\endgroup$ Commented Oct 15, 2015 at 15:36
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    $\begingroup$ @BrettChampion I think I will ignore you and just discuss this with my imaginary friend.. $\endgroup$ Commented Oct 15, 2015 at 15:55

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