Abs[x^a] == x^Re[a] /; x > 0

Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Abs", "[", SuperscriptBox["x", "a"], "]"]], "\[Equal]", SuperscriptBox["x", RowBox[List["Re", "[", "a", "]"]]]]], "/;", RowBox[List["x", ">", "0"]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <msup> <mi> x </mi> <mi> a </mi> </msup> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &#10869; </mo> <msup> <mi> x </mi> <mrow> <mi> Re </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> a </mi> <mo> ) </mo> </mrow> </msup> </mrow> <mo> /; </mo> <mrow> <mi> x </mi> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <abs /> <apply> <power /> <ci> x </ci> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> x </ci> <apply> <real /> <ci> a </ci> </apply> </apply> </apply> <apply> <gt /> <ci> x </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Abs", "[", SuperscriptBox["x_", "a_"], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["x", RowBox[List["Re", "[", "a", "]"]]], "/;", RowBox[List["x", ">", "0"]]]]]]]]

2001-10-29