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Associer des expressions littérales à une variable associées aux opérations sur les puissances à leur expression réduite    ressource 3461

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

a 9 a 10 1 a 4 a 30 1 a 5
A 1 = ( ( 1 a - 3 × a 1 ) × a 2 ) 5 TagBox[SuperscriptBox[RowBox[List["(", TagBox[RowBox[List[RowBox[List["(", TagBox[RowBox[List[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "3"]], HoldForm]], HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["1", HoldForm]], HoldForm]]], HoldForm], ")"]], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm]]], HoldForm], ")"]], "5"], HoldForm]
A 2 = 1 ( a 1 a - 3 a 3 ) 4 TagBox[FractionBox["1", SuperscriptBox[RowBox[List["(", TagBox[FractionBox[TagBox[FractionBox[TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["1", HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "3"]], HoldForm]], HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["3", HoldForm]], HoldForm]], HoldForm], ")"]], "4"]], HoldForm]
A 3 = a - 5 a 2 × a - 3 a - 5 TagBox[FractionBox[TagBox[RowBox[List[TagBox[FractionBox[TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "5"]], HoldForm]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["2", HoldForm]], HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "3"]], HoldForm]], HoldForm]]], HoldForm], TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "5"]], HoldForm]], HoldForm]], HoldForm]
A 4 = ( ( 1 a - 4 × a - 3 ) × a 4 ) 2 TagBox[SuperscriptBox[RowBox[List["(", TagBox[RowBox[List[RowBox[List["(", TagBox[RowBox[List[TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "4"]], HoldForm]], HoldForm]], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "3"]], HoldForm]], HoldForm]]], HoldForm], ")"]], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["4", HoldForm]], HoldForm]]], HoldForm], ")"]], "2"], HoldForm]
A 5 = ( 1 a - 1 ) 5 × a 4 TagBox[RowBox[List[TagBox[SuperscriptBox[RowBox[List["(", TagBox[FractionBox["1", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox[RowBox[List["-", "1"]], HoldForm]], HoldForm]], HoldForm], ")"]], "5"], HoldForm], " ", TagBox[SuperscriptBox[TagBox["a", HoldForm], TagBox["4", HoldForm]], HoldForm]]], HoldForm]