Question

Simplificar:
$2\sqrt[n]{4^{n+2} }$× $\sqrt[n]{2^{n-4} }$

a) 12 c) 2 e) 8
b) 16 d) 4

Answer 1

Saludos

Recuerda algunas propiedades:

  $a^{x} a^{y} =a^{x+y}$

  $\frac{a^{x} }{a^{y} } =a^{x-y}$

  $\sqrt[c]{a^{b} } =a^{\frac{b}{c} }$

En el problema: Simplificar

$M=2\sqrt[n]{4^{n+2} } \sqrt[n]{2^{n-4} }$

Primero vamos a descomponer:

• $2=2$

• $\sqrt[n]{4^{n+2} } =\sqrt[n]{(4^{n} )(4^{2}) } =(4^{\frac{n}{n} } )(16^{\frac{1}{n} } )=4(16^{\frac{1}{n} } )$

• $\sqrt[n]{2^{n-4} } =\sqrt[n]{(2^{n} )/(2^{4}) } =(2^{\frac{n}{n} } )/(16^{\frac{1}{n} } )=2/(16^{\frac{1}{n} } )$

Reemplazamos:

$M=2(4)(16^{\frac{1}{n} } )(\frac{2}{16^{\frac{1}{n} } } )$

Simplificamos $(16^{\frac{1}{n} } )$ :

$M=2(4)(2)$

$M=16$

El resultado es $16$