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    elige el número con exponente fraccionario que corresponde al radical

    Santiago

    Chicos, ¿alguien sabe la respuesta?

    obtenga elige el número con exponente fraccionario que corresponde al radical de este sitio.

    Elige El Número Con Exponente Fraccionario Que Corresponde Al Radical 307

    Encuentra respuesta a tu tarea ahora en "Tareas Gratis". Elige el número con exponente fraccionario que corresponde al radical. Asumiendo que la expresión es:30√x^7 El radical es propiamente la raíz cuadrada en este caso √x^7 sería el radicando (lo que está dentro de la raíz cuadrada)El # 2 sería el índice de la raíz (en este caso no aparece escrito porque se asume que es cuadrada)Una expresión de raíz cuadrada se puede colocar en forma de fracción:√a = (a)^(1/2)Donde:#1: es el numerador de la potencia y es puesto que es la potencia del término aquel está dentro de la raíz (radicando)#2: es el denominador de la potencia y se asocia de inmediato con el índice de la raíz (en este caso raíz cuadrada = 2 )Por lo tanto:30√x^7 = 30*(x)^(7/2) ⇒ exponente fraccionario del radicandoRecuerda marcar Mejor Respuesta si te gustó. Encuentra respuesta a tu tarea ahora en "Tareas Gratis".

    Elige El Número Con Exponente Fraccionario Que Corresponde Al Radical 307

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    Pregunta

    Elige el número con exponente fraccionario que corresponde al radical

    Respuesta

    Asumiendo que la expresión es:30√x^7 El radical es propiamente la raíz cuadrada en este caso √x^7 sería el radicando (lo que está dentro de la raíz cuadrada)El # 2 sería el índice de la raíz (en este caso no aparece escrito porque se asume que es cuadrada)Una expresión de raíz cuadrada se puede colocar en forma de fracción:√a = (a)^(1/2)Donde:#1: es el numerador de la potencia y es puesto que es la potencia del término aquel está dentro de la raíz (radicando)#2: es el denominador de la potencia y se asocia de inmediato con el índice de la raíz (en este caso raíz cuadrada = 2 )Por lo tanto:30√x^7 = 30*(x)^(7/2) ⇒ exponente fraccionario del radicandoRecuerda marcar Mejor Respuesta si te gustó

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    Exponentes Fraccionarios

    Exponentes FraccionariosObjetivo de Aprendizaje

    ·         Simplificar expresiones algebraicas con exponentes fraccionarios.

    Introducción

    Las raíces cuadradas a menudo se escriben usando un signo de radical:. Pero hay otra forma de representar el cálculo de una raíz. Podemos usar exponentes fraccionarios en lugar de un radical.

    ¿No te puedes imaginar cómo elevar un número a una potencia fraccionaria? Puede que sea difícil acostumbrarse, pero los exponentes fraccionarios pueden incluso ayudar a simplificar algunos problemas. Veamos cómo funcionan estos exponentes fraccionarios que llamamos radiales racionales.

    Fracciones en los Exponentes

    Los radicales y los exponentes son operaciones inversas. Por lo que puede sorprenderte un poco saber que un radial puede ser expresado como un número exponencial. La tabla de abajo muestra algunos ejemplos de raíces cuadradas comunes escritas como radicales, exponentes fraccionarios y enteros. Nota que el denominador de un exponente fraccionario es el número 2.

    RadicalExponenteEntero

    4 5 10

    Veamos otros ejemplos, pero esta vez con raíces cúbicas. Recuerda, el cubo de un número es el número elevado a la tercera potencia. Nota que en estos ejemplos, el denominador del exponente fraccionario es el número 3.

    RadicalExponenteEntero

    2 5 9

    Estos ejemplos nos ayudan a modelar una relación entre los radicales y los exponentes fraccionarios: a saber, que la enésima raíz de un número puede escribirse ya sea como  o.

    RadicalExponente

    … …

    "La raíz quinta del número 243" puede escribirse como:

    A) B) C) D)

    Mostrar/Ocultar la Respuesta

    Más Allá de Fracciones Unitarias

    Todos los numeradores de los exponentes fraccionarios en los ejemplos que hemos visto eran 1. Podemos usar otro tipo de exponentes además de fracciones unitarias, como se muestra abajo. ¿Notas algún patrón emergente en la tabla?

    RadicalExponente

    … …

    Para escribir un radical como un exponente fraccionario, la potencia a la cual elevamos la base se convierte en el numerador y la raíz se convierte en el denominador.

    Escribiendo Exponentes Fraccionarios

    Cualquier radical en la forma  pude escribirse como un exponente fraccionario en la forma.

    Esto también tiene sentido para nuestros exponentes con fracciones unitarias  puede escribirse como , ya que cualquier número sigue siendo el mismo si lo elevamos a la primera potencia. Ahora sabemos de dónde viene el numerador de 1 en la forma equivalente de .

    Trabajando con Exponentes Fraccionarios

    Los exponentes fraccionarios no son usados a menudo, además de las fórmulas avanzadas en los altos niveles de las matemáticas y la ciencia. Pero ocasionalmente son útiles para simplificar expresiones algebraicas.

    Exploremos algunas expresiones radicales para ver cómo. Aquí tenemos una expresión radicar que necesita ser simplificada, .

    Un método para simplificar esta expresión es factorizar y sacar grupos de 3, como se muestra:

    También podemos simplificar la expresión si pensamos en el radical como un exponente fraccionario, y usamos el principio de que cualquier radical en la forma  puede escribirse como un exponente fraccionario en la forma :

    Nota que los exponentes fraccionarios están sometidos a las mismas reglas que los exponentes que aparecen en expresiones algebraicas.

    Ambos métodos de simplificación nos dan el mismo resultado, 2. Dependiendo del contexto del problema, podría ser más fácil usar un método u el otro, por ahora, notemos que fuimos capaces de simplificar esta expresión más rápido usando exponentes fraccionarios que usando el método de "sacar".

    Intentemos una expresión más complicada, ¡Caray! Esta expresión tiene dos variables, una fracción, y un radical. Es un poco intimidante. La tomaremos paso a paso para ver si el usar exponentes fraccionarios nos puede ayudar a simplificarla.

    Empezaremos por simplificar el denominador porque es en donde se localiza el radical.

    EjemploProblema

    Simplificar

    Separar los términos del denominador

    Calcular la raíz de 8, que es 2

    Reescribir el radical como un exponente

    Reescribir la fracción como una serie de factores con el fin de cancelar términos (ve el siguiente paso)

    Simplificar la constante y términos

    Usar la regla de los exponentes negativos,

    -, para reescribir  como

    Combinar los términos b al sumar los exponentes

    Regresar el exponente a su forma radical. Por convención, una expresión no se considera simplificada si tiene un exponente fraccionario o un radical en el denominador

    Bueno, eso tomó un rato, pero lo logramos. Aplicamos lo que sabemos sobre exponentes fraccionarios, exponentes negativos y las reglas de los exponentes para simplificar la expresión.

    Simplificar A) B) C) D)

    Mostrar/Ocultar la Respuesta

    Sumario

    Un radical puede ser expresado como un valor con un exponente fraccionario siguiendo la convención =. Reescribir radiales como exponentes fraccionarios puede ser útil para simplificar algunas expresiones radicales. Cuando trabajes con exponentes fraccionarios, recuerda que están sujetos a todas las reglas de los otros exponentes que aparecen en expresiones algebraicas.

    fuente : content.nroc.org

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    fuente : brainly.lat

    ¿Quieres ver la respuesta o más?
    Santiago 15 day ago
    4

    Chicos, ¿alguien sabe la respuesta?

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