Question

Simplifique a expressão : 2^n+4 - 2×2^2n/2×2^n+3

Answer 1

$\frac{{2}^{n+4}-2.{2}^{2n}}{2.{2}^{n+3}}$

$\frac{{2}^{n}.{2}^{4}-{2}. {2}^{n}.{2}^{n}}{{2}^{n}. {2}^{4}}$

$\frac{\cancel{{2}^{n}}({2}^{4}-2.{2}^{n})}{\cancel{{2}^{n}}.{2}^{4}}$

$\frac{16-{2}^{n+1}}{16}$

$\frac{16}{16}-\frac{{2}^{n+1}}{16}$

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

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

$\boxed{\boxed{\frac{{2}^{n+4}-2.{2}^{2n}}{2.{2}^{n+3}}=1-{2}^{n-3}}}$

Answer 2

Resposta:

A expressão correta é assim

${2^{n+4}-2.2^{n}\over2.2^{n+3}}=\\ \\ desmembrando\\ \\ {2^n.2^4-2.2^n\over2.2^n.2^3}=\\ \\ {2^n.2^4-2.2^n\over2^4.2^n}=\\ \\ colocar~~ 2^n~~como~~fator~~comum\\ \\ {2^n(2^4-2)\over2^n.2^4}=\\ \\ Cancelar~~2^n\\ \\ {(2^4-2)\over2^4}={(16-2)\over16}={14\over16}={7\over8}$