$ a/b c/d stackrel((-4))=(ac)/(bd)$
| $ (ab)(cd)stackrel((-3))= abcd$
| $ abstackrel((-2))=ba$
| $(ka)/(kb)stackrel((-1))=a/b$
|
$a^mstackrel((0))=...aaaaaaa...$
| $a^m a^n stackrel((1))=a^(m+n)$
| $a^m/a^n stackrel((2))=a^(m-n)$
| $(a^m)^n stackrel((3))=a^("m·n")$
| $(ab)^n stackrel((4))= a^nb^n$
| $(a/b)^nstackrel((5))=a^n/b^n$
|
$(a^0)stackrel((!))=1$
| $a^(-n)stackrel((6))=1/a^n$
|
$a^(1/n)stackrel((7))=root(n)(a)$
| $a^(m/n)stackrel((8))=root(n)(a^m)$
| $root(m)(ab)stackrel((9))=root(m)(a)root(m)(b)
| $root(m)(a/b)stackrel((10))=root(m)(a)/root(m)(b)
| $root(k)(..) + root(m)(..) + root(n)(..)stackrel((11))= (a+b+c)root(p)(.....)$
|
$a>b stackrel((12))(iff) a+-k>b+-k$
| $a>b ; k>0 stackrel((13))(iff) ka>kb $
| $a>b ; k<0 stackrel((14))(iff) ka
$("expr"_1)/("expr"_2) stackrel((15))(<=) 0 rarr [ ("segno(expr1): --------------|_________"), ("segno(expr2): ________________|-------"), ("sgn(expr1/expr2): ---------|____|-------"), (I_1: "soluzione(........): ////////////|..........|//////////")]$
| ${ ("diseq"_1), ("diseq"_2), ("diseq"_3):} stackrel((16))rarr "Soluzione="(I_1capI_2capI_3)$
| |