(Sqrt[x] Sqrt[y])^a == x^(a/2) y^(a/2)

Cell[BoxData[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox["x"], SqrtBox["y"]]], ")"]], "a"], "\[Equal]", RowBox[List[SuperscriptBox["x", RowBox[List["a", "/", "2"]]], " ", SuperscriptBox["y", RowBox[List["a", "/", "2"]]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msqrt> <mi> x </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> y </mi> </msqrt> </mrow> <mo> ) </mo> </mrow> <mi> a </mi> </msup> <mo> &#63449; </mo> <mrow> <msup> <mi> x </mi> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <msup> <mi> y </mi> <mrow> <mi> a </mi> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <power /> <apply> <times /> <apply> <power /> <ci> x </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> y </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> a </ci> </apply> <apply> <times /> <apply> <power /> <ci> x </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> y </ci> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", SuperscriptBox[RowBox[List["(", RowBox[List[SqrtBox["x_"], " ", SqrtBox["y_"]]], ")"]], "a_"], "]"]], "\[RuleDelayed]", RowBox[List[SuperscriptBox["x", RowBox[List["a", "/", "2"]]], " ", SuperscriptBox["y", RowBox[List["a", "/", "2"]]]]]]]]]

2007-05-02