Question

Função Exponencial, me ajudem por favor!

Simplifique:
a)2^n+4 - 2 X 2^n/ 2 X 2^n+3

b) (2^n + 2^n-1) (3n-3^n-1)

OBS: Me mostre passo a passo da resolução, por favor!

Answer 1

a)

$\frac{2^{n+4}-2.2^n}{2.2^{n+3}}\\ \\ \frac{2^n.2^4-2.2^n}{2.2^n.2^3}\\ \\ \frac{16.2^n-2.2^n}{16.2^n}\\ \\ \frac{14.2^n}{16.2^n}=\frac{14}{16}=\frac{7}{8}$

b)

$(2^n+2^{n-1})(3^n-3^{n-1})=\\ \\ (2^n+\frac{2^n}{2})(3^n-\frac{3^n}{3})=\\ \\ (\frac{2.2^n+2^n}{2})(\frac{3.3^n-3^n}{3})=\\ \\ (\frac{3.2^n}{2})(\frac{2.3^n}{3})=\\ \\ \frac{6.2^n.3^n}{6}=\\ \\ 2^n.3^n=6^n$