Question

$\frac{ 2^{n+ 4} + 2^{n+ 2} + 2^{n -1}} { 2^{n-2} + 2^{n-1} }$

Answer 1

$\frac{2^{n+4}+2^{n+2}+2^{n-1}}{2^{n-2}+2^{n-1}} \\ \\=\frac{2^n\cdot2^4+2^n\cdot2^2+2^n\cdot2^{-1}}{2^n\cdot2^{-2}+2^n\cdot2^{-1}} \\ \\= \frac{2^n\cdot(2^4+2^2+2^{-1})}{2^n\cdot(2^{-2}+2^{-1})} \\ \\= \frac{16+4+ \frac{1}{2}}{(\frac{1}{2})^2+\frac{1}{2}} \\ \\= \frac{20+ \frac{1}{2}}{\frac{1}{4}+\frac{1}{2}} \\ \\= \frac{\frac{40}{2}+ \frac{1}{2}}{\frac{1}{4}+\frac{2}{4}} \\ \\= \frac{\frac{40+1}{2}}{\frac{1+2}{4}}= \frac{41/2}{3/4}= \frac{41}{2}\cdot \frac{4}{3}= \frac{164^{:2}}{6_{:2}}$
$= \frac{82}{2}$