Rescrie \large{\dfrac{expr(NUM)}{expr(DEN)}}
sub forma
\large{BASE1^nBASE2^m}
.
Putem presupune că BASE1\neq 0, BASE2\neq 0
.
Putem începe prin a simplifica numărătorul si numitorul separat.
Putem folosi proprietatea ridicarii unei puteri la altă putere la numărător:
(\blue{expr(NUM1)}\green{expr(NUM2)})^{EXPNUM3} =
\blue{expr(['^', NUM1, EXPNUM3])}\green{expr(['^', NUM2, EXPNUM3])}
\blue{expr(['^', NUM1, EXPNUM3]) = NUMHINT1}
\green{expr(['^', NUM2, EXPNUM3]) = NUMHINT2}
Așadar,
(\blue{expr(NUM1)}\green{expr(NUM2)})^{EXPNUM3} =
\blue{NUMHINT1}\green{NUMHINT2}
.
Putem folosi proprietatea ridicarii unei puteri la altă putere la numitor:
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3} =
\blue{expr(["^", DEN1, EXPDEN3])}\green{expr(["^", DEN2, EXPDEN3])}
\blue{expr(['^', DEN1, EXPDEN3]) = DENHINT1}
\green{expr(['^', DEN2, EXPDEN3]) = DENHINT2}
Așadar:
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3} =
\blue{DENHINT1}\green{DENHINT2}
.
Rezultă:
\dfrac{
(\blue{expr(NUM1)}\green{expr(NUM2)})^{EXPNUM3}
\blue{expr(NUM1)}\green{expr(NUM2)}
}{
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3}
\blue{expr(DEN1)}\green{expr(DEN2)}
} = \dfrac{\blue{NUMHINT1}\green{NUMHINT2}}{
\blue{DENHINT1}\green{DENHINT2}}
.
Acum putem împărții fracția în două, una pentru fiecare variabilă:
\dfrac{\blue{NUMHINT1}\green{NUMHINT2}}{\blue{DENHINT1}\green{DENHINT2}} =
\blue{\dfrac{NUMHINT1}{DENHINT1}} \cdot \green{\dfrac{NUMHINT2}{DENHINT2}} =
\blue{BASE1^{EXPNUM1 * EXPNUM3 - negParens(EXPDEN1 * EXPDEN3)}} \cdot
\green{BASE2^{EXPNUM2 * EXPNUM3 - negParens(EXPDEN2 * EXPDEN3)}} =
expr(ANS)
Rescrie \large{\dfrac{expr(NUM)}{expr(DEN)}}
sub forma
\large{BASE1^nBASE2^m}
.
Putem presupune că BASE1\neq 0, BASE2\neq 0
.
Putem începe prin a simplifica numărătorul si numitorul separat.
Putem folosi proprietatea ridicarii unei puteri la altă putere la numărător:
\blue{expr(['^', NUM1, EXPNUM3])} = \blue{NUMHINT1}
Putem folosi proprietatea ridicarii unei puteri la altă putere la numitor:
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3} =
\blue{expr(["^", DEN1, EXPDEN3])}\green{expr(["^", DEN2, EXPDEN3])}
\blue{expr(['^', DEN1, EXPDEN3]) = DENHINT1}
\green{expr(['^', DEN2, EXPDEN3]) = DENHINT2}
So,
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3} =
\blue{DENHINT1}\green{DENHINT2}
.
Rezultă:
\dfrac{
(\blue{expr(NUM1)})^{EXPNUM3}
\blue{expr(NUM1)}
}{
(\blue{expr(DEN1)}\green{expr(DEN2)})^{EXPDEN3}
\blue{expr(DEN1)}\green{expr(DEN2)}
} = \dfrac{\blue{NUMHINT1}}{
\blue{DENHINT1}\green{DENHINT2}}
.
Acum putem împărții fracția în două, una pentru fiecare variabilă:
\dfrac{\blue{NUMHINT1}}{\blue{DENHINT1}\green{DENHINT2}} =
\blue{\dfrac{NUMHINT1}{DENHINT1}} \cdot \green{\dfrac{1}{DENHINT2}} =
\blue{BASE1^{EXPNUM1 * EXPNUM3 - negParens(EXPDEN1 * EXPDEN3)}} \cdot
\green{BASE2^{ - negParens(EXPDEN2 * EXPDEN3)}} =
expr(ANS)