Question

Reduza a forma mais simples

$\frac{ 2^{x+3} *2- 2^{x-1}*7 }{5*2 ^{x-4} }$

Answer 1

Olá


Propriedades que serão utilizadas:

$\mathsf{a^{b+c}~=~a^b\cdot a^c}$


$\displaystyle\mathsf{a^{-b}~=~ \frac{1}{a^b} }$




Desenvolvendo


$\displaystyle\mathsf{ \frac{2^{x+3}\cdot 2-2^{x-1}\cdot7}{5\cdot 2^{x-4}} }\\\\\\\mathsf{ \frac{2^x\cdot2^3\cdot2-2^x\cdot2^{-1}\cdot7}{5\cdot 2^x\cdot2^{-4}} }\\\\\\\mathsf{ \frac{2^x\cdot2^4-2^x\cdot2^{-1}\cdot7}{5\cdot 2^x\cdot2^{-4}} }\\\\\\\mathsf{colocando~ o~ 2^x ~em ~evidencia}\\\\\\\mathsf{ \frac{2^x(2^4-2^{-1}\cdot7)}{2^x\cdot (5\cdot2^{-4})} }\\\\\\\text{Simplifica}\\\\\\\mathsf{ \frac{\diagup\!\!\!\!{2^x}(2^4-2^{-1}\cdot7)}{\diagup\!\!\!\!\!{2^x}\cdot (5\cdot2^{-4})} }$

$\displaystyle \\\\\\\mathsf{ \frac{2^4-2^{-1}\cdot7}{5\cdot2^{-4}} }\\\\\\\mathsf{ \frac{16- \frac{1}{2}\cdot 7 }{5\cdot \frac{1}{2^4} } }\\\\\\\mathsf{ \frac{16- \frac{7}{2} }{ \frac{5}{16} } }\\\\\\\text{Tira o MMC entre as fracoes no numerador}\\\\\\\mathsf{ \frac{\frac{25}{2} }{ \frac{5}{16} } }$


Divisão de frações, divide a primeira pelo inverso da segunda.


$\displaystyle \mathsf{ \frac{25}{2} \cdot \frac{16}{5} }\\\\\\\mathsf{ \frac{400}{10} }\\\\\\\boxed{40}$