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Oct 28, 2014 at 16:48 comment added celtschk @ChipHurst: Both seem not to be available at Mathematica 8; however I've found them in the web documentation. CubeRoot clearly wouldn't be a replacement for realpower, covering only the very special case $x^{1/3}$. Surd (which IMHO is a contender for the most unintuitively named Mathematica function) gives the more general case $x^{1/n}$; while it would certainly be a better building block for realpower, it's however not a full replacement because it doesn't handle e.g. $x^{2/3}$ (which is the case from the question).
Oct 28, 2014 at 15:42 comment added Greg Hurst Instead of realpower, you should look into Surd and CubeRoot.
Oct 23, 2014 at 17:30 comment added An old man in the sea. Ok. Many thanks ;)
Oct 23, 2014 at 16:33 comment added celtschk @Anoldmaninthesea.: Actually, it is not the representation, but the definition of the complex power. It's just easiest described in the polar representation (most probably, internally the formula $x^y=\exp(y\ln x)$ is used, together with an appropriate branch cut for $\ln x$). However see my edit for a function that does what you want (but probably has a lot of room for improvement).
Oct 23, 2014 at 16:32 history edited celtschk CC BY-SA 3.0
added a way to get the real power
Oct 23, 2014 at 16:20 comment added An old man in the sea. Also, thanks for you answer.
Oct 23, 2014 at 16:20 vote accept An old man in the sea.
Oct 23, 2014 at 16:16 comment added An old man in the sea. So, by default it represents the number in polar form. Is there a way to make plot use real numbers usual representation only? Because the left side is still missing...
Oct 23, 2014 at 16:06 history edited celtschk CC BY-SA 3.0
fixed broken formulas
Oct 23, 2014 at 16:00 history answered celtschk CC BY-SA 3.0