z^(Subscript[a, 1] Subscript[a, 2]) == (z^Subscript[a, 1])^Subscript[a, 2] /; Inequality[-Pi, Less, Im[Subscript[a, 1] Log[z]], LessEqual, Pi] || Inequality[-1, Less, Subscript[a, 1], LessEqual, 1] || Element[Subscript[a, 2], Integers]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <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> <mo> &#10869; </mo> <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> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mi> &#960; </mi> </mrow> <mo> &lt; </mo> <mrow> <mi> Im </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mi> &#960; </mi> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <msub> <mi> a </mi> <mn> 1 </mn> </msub> <mo> &#8804; </mo> <mn> 1 </mn> </mrow> <mo> &#8744; </mo> <mrow> <msub> <mi> a </mi> <mn> 2 </mn> </msub> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <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> <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> <apply> <or /> <apply> <ci> Inequality </ci> <apply> <times /> <cn type='integer'> -1 </cn> <pi /> </apply> <lt /> <apply> <imaginary /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ln /> <ci> z </ci> </apply> </apply> </apply> <leq /> <pi /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> -1 </cn> <lt /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 1 </cn> </apply> <leq /> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <apply> <ci> Subscript </ci> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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

2001-10-29