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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Transformations > Products, sums, and powers of the direct function > Power of the direct function





http://functions.wolfram.com/01.02.16.0124.01









  


  








Input Form





(z^m)^(1/n) == (z^(m/n) (-1)^(1/n))/(E^((I (-1 + 2 k) Pi)/m))^(m/n) /; Element[m, Integers] || (m > 0 && Element[n, Integers]) || (n > 0 && Inequality[((2 k - 3) Pi)/m, Less, Arg[z], LessEqual, ((2 k - 1) Pi)/m] && 1 <= k <= Floor[(m + 1)/2])








Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <msup> <mrow> <mo> ( </mo> <msup> <mi> z </mi> <mi> m </mi> </msup> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> n </mi> </mrow> </msup> <mo> &#10869; </mo> <mrow> <msup> <mi> z </mi> <mrow> <mi> m </mi> <mo> / </mo> <mi> n </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <msup> <mi> &#8519; </mi> <mfrac> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mi> m </mi> </mfrac> </msup> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mfrac> <mi> m </mi> <mi> n </mi> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 1 </mn> <mo> / </mo> <mi> n </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> m </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &#8712; </mo> <semantics> <msup> <mi> &#8469; </mi> <mo> + </mo> </msup> <annotation encoding='Mathematica'> TagBox[SuperscriptBox[&quot;\[DoubleStruckCapitalN]&quot;, &quot;+&quot;], Function[Integers]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 3 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mi> m </mi> </mfrac> <mo> &lt; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> k </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> &#960; </mi> </mrow> <mi> m </mi> </mfrac> </mrow> <mo> &#8743; </mo> <mrow> <mn> 1 </mn> <mo> &#8804; </mo> <mi> k </mi> <mo> &#8804; </mo> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <mi> m </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <power /> <ci> z </ci> <ci> m </ci> </apply> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <exponentiale /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> <pi /> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> m </ci> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -3 </cn> </apply> <pi /> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> <lt /> <apply> <arg /> <ci> z </ci> </apply> <leq /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <cn type='integer'> -1 </cn> </apply> <pi /> <apply> <power /> <ci> m </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <leq /> <cn type='integer'> 1 </cn> <ci> k </ci> <apply> <floor /> <apply> <times /> <apply> <plus /> <ci> m </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02