3. Упростить: 14^n/(2^(n−2) · 7^n); 36^(n+1)/6^(2n+1); (x^(6n)y^(n+3))/(x^(2n)y^(n+4)); (6^(n+1)+6^(n+3))/37.

1. \(\frac{14^n}{2^{n-2}\cdot7^n}=\frac{2^n7^n}{2^{n-2}7^n}=2^{n-(n-2)}=2^2=4\).
2. \(\frac{36^{n+1}}{6^{2n+1}}=\frac{(6^2)^{n+1}}{6^{2n+1}}=6^{2n+2-(2n+1)}=6\).
3. \(\frac{x^{6n}y^{n+3}}{x^{2n}y^{n+4}}=x^{4n}y^{-1}=\frac{x^{4n}}{y}\).
4. \(\frac{6^{n+1}+6^{n+3}}{37}=\frac{6^{n+1}(1+6^2)}{37}=\frac{37\cdot6^{n+1}}{37}=6^{n+1}\).

Ответ: 4; 6; \(\frac{x^{4n}}{y}\); \(6^{n+1}\).