Question

Resolva a expressão.

Answer 1

E aí mano,

use as propriedades da exponenciação:

$a^{-m}= \dfrac{1}{a^m}\\\\ a^{m+n}=a^m\cdot a^n$

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$\dfrac{2^x+2^{x+1} +2^{x+2}}{2^{x-1}+2^{x+3}}= \dfrac{2^x+2^x\cdot2^1+2^x\cdot2^2}{2^x\cdot2^{-1}+2^x\cdot2^3}\\\\\\ \dfrac{2^x+2^{x+1}+2^{x+2}}{2^{x-1}+2^{x+3}} = \dfrac{\not2^x\cdot(1+2^1+2^2)}{\not2^x\cdot(2^{-1}+2^3)}\\\\\\ \dfrac{2^{x}+2^{x+1}+2^{x+2}}{2^{x-1}+2^{x+3}}= \dfrac{1+2+4}{ \dfrac{1}{2}+8 }$

$\dfrac{2^x+2^{x+1}+2^{x+2}}{2^{x-1}+2^{x+3}}= \dfrac{7}{ \dfrac{17}{2} }\\\\\\ \dfrac{2^x+2^{x+1}+2^{x+2}}{2^{x-1}+2^{x+3}}= 7\div\dfrac{17}{2}\\\\\\ \Large\boxed{\boxed{\boxed{\dfrac{2^x+2^{x+1}+2^{x+2}}{2^{x-1}+2^{x+3}}= \dfrac{14}{17}}}}.\\.$

FLWW MANO!