randVar( ) randVar( ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) randRangeNonZero( -5, 5 ) [ "^", [ "*", [ "^", BASE1, EXPDEN1 ], [ "^", BASE2, EXPDEN2 ] ], EXPDEN3 ] [ "*", [ "^", [ "^", BASE1, EXPDEN1 ], EXPDEN3 ], [ "^", [ "^", BASE2, EXPDEN2 ], EXPDEN3 ] ] [ "*", [ "^", BASE1, EXPDEN1 * EXPDEN3 ], [ "^", BASE2, EXPDEN2 * EXPDEN3 ] ]
randRangeNonZero( -5, 5 ) [ "^", [ "*", [ "^", BASE1, EXPNUM1 ], [ "^", BASE2, EXPNUM2 ] ], EXPNUM3 ] [ "*", [ "^", [ "^", BASE1, EXPNUM1 ], EXPNUM3 ], [ "^", [ "^", BASE2, EXPNUM2 ], EXPNUM3 ] ] [ "*", [ "^", BASE1, EXPNUM1 * EXPNUM3 ], [ "^", BASE2, EXPNUM2 * EXPNUM3 ] ] EXPNUM1 * EXPNUM3 - EXPDEN1 * EXPDEN3 EXPNUM2 * EXPNUM3 - EXPDEN2 * EXPDEN3 [ "*", [ "^", BASE1, EXP1 ], [ "^", BASE2, EXP2 ] ]

Simplifica; expresa tu respuesta en forma exponencial. Asume BASE1\neq 0, BASE2\neq 0.

\dfrac{\blue{expr( NUM )}}{\green{expr( DEN )}}

BASE1EXP1BASE2EXP2

Introduce un número entero (posiblemente negativo) para cada exponente

Para empezar trata de simplificar el numerador y el denominador independientemente.

En el numerador, podemos usar la propiedad distributiva de los exponentes.

\blue{expr( NUM ) = expr( NUMHINT1 )}.

A la izquierda tenemos \blue{expr( [ "^", BASE1, EXPNUM1 ] )} elevado al exponente \blue{EXPNUM3}. Como \blue{EXPNUM1 \times EXPNUM3 = EXPNUM1 * EXPNUM3}, entonces \blue{expr( [ "^", [ "^", BASE1, EXPNUM1 ], EXPNUM3 ] ) = expr( [ "^", BASE1, EXPNUM1 * EXPNUM3 ] )}.

Aplica las ideas anteriores para simplificar la ecuación.

\dfrac{\blue{expr( NUM )}}{\green{expr( DEN )}} = \dfrac{\blue{expr( NUMHINT2 )}}{\green{expr( DENHINT2 )}}.

Separa la ecuación por variable y simplifica.

\dfrac{\blue{expr( NUMHINT2 )}}{\green{expr( DENHINT2 )}} = \dfrac{\blue{expr( [ "^", BASE1, EXPNUM1 * EXPNUM3 ] )}}{\green{expr( [ "^", BASE1, EXPDEN1 * EXPDEN3 ] )}} \cdot \dfrac{\blue{expr( [ "^", BASE2, EXPNUM2 * EXPNUM3 ] )}}{\green{expr( [ "^", BASE2, EXPDEN2 * EXPDEN3 ] )}} = BASE1^{\blue{EXPNUM1 * EXPNUM3} - \green{negParens( EXPDEN1 * EXPDEN3 )}} \cdot BASE2^{\blue{EXPNUM2 * EXPNUM3} - \green{negParens( EXPDEN2 * EXPDEN3 )}} = expr( ANS )

0 [ "^", [ "^", BASE1, EXPNUM1 ], EXPNUM3 ] [ "^", [ "^", BASE1, EXPNUM1 ], EXPNUM3 ] [ "^", BASE1, EXPNUM1 * EXPNUM3 ] EXPNUM1 * EXPNUM3 - EXPDEN1 * EXPDEN3 EXPNUM2 * EXPNUM3 - EXPDEN2 * EXPDEN3 [ "*", [ "^", BASE1, EXP1 ], [ "^", BASE2, EXP2 ] ]

Simplifica; expresa tu respuesta en forma exponencial. Asume BASE1\neq 0, BASE2\neq 0.

\dfrac{\blue{expr( NUM )}}{\green{expr( DEN )}}

BASE1EXP1BASE2EXP2

Introduce un número entero (posiblemente negativo) para cada exponente

Para empezar trata de trabajar independientemente en el numerador y el denominador.

En el numerador tenemos \blue{expr( [ "^", BASE1, EXPNUM1 ] )} elevado al exponente \blue{EXPNUM3}. Como \blue{EXPNUM1 \times EXPNUM3 = EXPNUM1 * EXPNUM3}, entonces \blue{expr( NUM ) = expr( NUMHINT2 )}.

En el denominador podemos usar la propiedad distributiva de los exponentes.

\green{expr( DEN ) = expr( DENHINT1 )}.

Simplifica utilizando el mismo método que usaste en el numerador y después junta las distintas partes de la ecuación.

\dfrac{\blue{expr( NUM )}}{\green{expr( DEN )}} = \dfrac{\blue{expr( NUMHINT2 )}}{\green{expr( DENHINT2 )}}.

Separa la ecuación por variable y simplifica.

\dfrac{\blue{expr( NUMHINT2 )}}{\green{expr( DENHINT2 )}} = \dfrac{\blue{expr( [ "^", BASE1, EXPNUM1 * EXPNUM3 ] )}}{\green{expr( [ "^", BASE1, EXPDEN1 * EXPDEN3 ] )}} \cdot \dfrac{\blue{1}}{\green{expr( [ "^", BASE2, EXPDEN2 * EXPDEN3 ] )}} = BASE1^{\blue{EXPNUM1 * EXPNUM3} - \green{negParens( EXPDEN1 * EXPDEN3 )}} \cdot BASE2^{- \green{negParens( EXPDEN2 * EXPDEN3 )}} = expr( ANS ).