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Associer des expressions littérales à deux variables associées aux opérations sur les puissances à leur expression réduite    ressource 3462

Soit a et b deux nombres non nuls. Associez à chacun des nombres A i (où i est un entier compris entre 1 et 5) l'expression réduite correspondante.

a 12 b 4 1 a 20 b 5 1 a 36 a 2 b 11 a 20
A 1 = 1 ( 1 ( 1 a 5 a - 2 ) 3 ) 4 TagBox[FractionBox["1", SuperscriptBox[RowBox[List["(", TagBox[FractionBox["1", SuperscriptBox[RowBox[List["(", TagBox[FractionBox[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["5", HoldForm]], HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "2"]], HoldForm]], HoldForm]], HoldForm], ")"]], "3"]], HoldForm], ")"]], "4"]], HoldForm]
A 2 = ( 1 a 4 b 1 ) 5 TagBox[SuperscriptBox[RowBox[List["(", TagBox[FractionBox[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["4", HoldForm]], HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["b", HoldForm], TagBox["1", HoldForm]], HoldForm]], HoldForm], ")"]], "5"], HoldForm]
A 3 = ( ( 1 b - 2 × b 4 ) × b 5 ) × a 2 TagBox[RowBox[List[RowBox[List["(", TagBox[RowBox[List[RowBox[List["(", TagBox[RowBox[List[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["b", HoldForm], TagBox[RowBox[List["-", "2"]], HoldForm]], HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["b", HoldForm], TagBox["4", HoldForm]], HoldForm]]], HoldForm], ")"]], " ", TagBox[SuperscriptBox[TagBox["b", HoldForm], TagBox["5", HoldForm]], HoldForm]]], HoldForm], ")"]], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm]]], HoldForm]
A 4 = ( a 2 × a 2 ) 5 TagBox[SuperscriptBox[RowBox[List["(", TagBox[RowBox[List[TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm]]], HoldForm], ")"]], "5"], HoldForm]
A 5 = ( 1 b 2 a - 4 × a 2 ) 2 TagBox[SuperscriptBox[RowBox[List["(", TagBox[RowBox[List[TagBox[FractionBox[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["b", HoldForm], TagBox["2", HoldForm]], HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "4"]], HoldForm]], HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm]]], HoldForm], ")"]], "2"], HoldForm]