Simplify and hence find the value of n: `(3^(2n)9^(2)3^(-n))/(3^(3n))` = 27

Find the value of Q ((n+3)!)/((n+1)!)

If n! +(n-1) ! =3, then find the value of n.

Find the value of sum_(n=1)^(infty) 1/(2n-1) (1/9^(n-1) + 1/9^(2n-1))

If ""^(n)a^(n) and ""^(n)b^(n) are rational numbers and (3+sqrt5)/(3-sqrt5)=-a+bsqrt5 , find the value of ""^(n)a^(n) and ""^(n) b^(n) .