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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Transformations > Power of arguments > With respect to z





http://functions.wolfram.com/01.02.16.0097.01









  


  








Input Form





(z^Subscript[a, 1])^Subscript[a, 2] == z^(Subscript[a, 1] Subscript[a, 2]) /; Element[Subscript[a, 1], Reals] && Inequality[-Pi, Less, Subscript[a, 1] Arg[z], LessEqual, Pi]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", SuperscriptBox["z", SubscriptBox["a", "1"]], ")"]], SubscriptBox["a", "2"]], "\[Equal]", SuperscriptBox["z", RowBox[List[SubscriptBox["a", "1"], " ", SubscriptBox["a", "2"]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List[SubscriptBox["a", "1"], ",", "Reals"]], "]"]], "\[And]", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[SubscriptBox["a", "1"], " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]]








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> <msub> <mi> a </mi> <mn> 1 </mn> </msub> </msup> <mo> ) </mo> </mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </msup> <mo> &#10869; </mo> <msup> <mi> z </mi> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> a </mi> <mn> 2 </mn> </msub> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> &#8804; </mo> <mi> &#960; </mi> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <power /> <ci> z </ci> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <reals /> </apply> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <arg /> <ci> z </ci> </apply> </apply> <leq /> <pi /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", SuperscriptBox["z_", SubscriptBox["a_", "1"]], ")"]], SubscriptBox["a_", "2"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["z", RowBox[List[SubscriptBox["aa", "1"], " ", SubscriptBox["aa", "2"]]]], "/;", RowBox[List[RowBox[List[SubscriptBox["aa", "1"], "\[Element]", "Reals"]], "&&", RowBox[List[RowBox[List["-", "\[Pi]"]], "<", RowBox[List[SubscriptBox["aa", "1"], " ", RowBox[List["Arg", "[", "z", "]"]]]], "\[LessEqual]", "\[Pi]"]]]]]]]]]]


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





2007-05-02