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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 product of the direct function





http://functions.wolfram.com/01.02.16.0132.01









  


  








Input Form





((-1)^r z^r)^b == (-1)^(b r) z^(b r) /; Element[r, Reals] && Inequality[0, Less, r, LessEqual, 1/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r"], " ", SuperscriptBox["z", "r"]]], ")"]], "b"], " ", "\[Equal]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["b", " ", "r"]]], SuperscriptBox["z", RowBox[List["b", " ", "r"]]]]]]], "/;", RowBox[List[RowBox[List["r", "\[Element]", "Reals"]], "\[And]", RowBox[List["0", "<", "r", "\[LessEqual]", FractionBox["1", "2"]]]]]]]]]








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> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> r </mi> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> <mi> b </mi> </msup> <mo> &#63449; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> z </mi> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> r </mi> </mrow> </msup> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> r </mi> <mo> &#8712; </mo> <semantics> <mi> &#8477; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalR]&quot;, Function[List[], Reals]] </annotation> </semantics> </mrow> <mo> &#8743; </mo> <mrow> <mn> 0 </mn> <mo> &lt; </mo> <mi> r </mi> <mo> &#8804; </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <ci> r </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <ci> b </ci> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> r </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <ci> b </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> r </ci> <reals /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 0 </cn> <lt /> <ci> r </ci> <leq /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "r_"], " ", SuperscriptBox["z_", "r_"]]], ")"]], "b_"], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["b", " ", "r"]]], " ", SuperscriptBox["z", RowBox[List["b", " ", "r"]]]]], "/;", RowBox[List[RowBox[List["r", "\[Element]", "Reals"]], "&&", RowBox[List["0", "<", "r", "\[LessEqual]", FractionBox["1", "2"]]]]]]]]]]]


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





2007-05-02