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Power




Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Transformations > Multiple arguments > With respect to z > For quotients





http://functions.wolfram.com/01.02.16.0021.01









  


  








Input Form





(Subscript[z, 1]/Subscript[z, 2])^a == (Subscript[z, 1]/(Subscript[z, 2] - Subscript[z, 1]))^a/ (Subscript[z, 2]/(Subscript[z, 2] - Subscript[z, 1]))^a /; Element[Subscript[z, 2] - Subscript[z, 1], Reals] && Subscript[z, 2] != Subscript[z, 1]








Standard Form





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








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> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <msub> <mi> z </mi> <mn> 2 </mn> </msub> </mfrac> <mo> ) </mo> </mrow> <mi> a </mi> </msup> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <msup> <mrow> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> a </mi> </msup> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <msub> <mi> z </mi> <mn> 1 </mn> </msub> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mfrac> <mo> ) </mo> </mrow> <mi> a </mi> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> - </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> z </mi> <mn> 2 </mn> </msub> <mo> &#8800; </mo> <msub> <mi> z </mi> <mn> 1 </mn> </msub> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> a </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> a </ci> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <reals /> </apply> <apply> <neq /> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <ci> Subscript </ci> <ci> z </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["z_", "1"], SubscriptBox["z_", "2"]], ")"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["zz", "1"], RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]]], ")"]], "a"], SuperscriptBox[RowBox[List["(", FractionBox[SubscriptBox["zz", "2"], RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]]], ")"]], "a"]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["zz", "2"], "-", SubscriptBox["zz", "1"]]], "\[Element]", "Reals"]], "&&", RowBox[List[SubscriptBox["zz", "2"], "\[NotEqual]", SubscriptBox["zz", "1"]]]]]]]]]]]


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





2001-10-29