Evaluate :`(a^(2n+1) xx a^((2n+1)(2n-1)))/(a^(n(4n-1)) xx (a^2)^(2n+3)`

Find the value of (3^(n)xx3^(2n+1))/(9^(n)xx3^(n-1)) .

(3xx9^(n+1)-9xx3^(2n))/(3xx3^(2n+3)-9^(n+1))

Find the value of n : (2^(3)xx5^(n+1)xx10^(2)xx5^(n-1))/(125xx5^(n-2)xx2^(7))=(25)/(4)

Find the sum of series upto n terms ((2n+1)/(2n-1))+3((2n+1)/(2n-1))^(2)+5((2n+1)/(2n-1))^(3)+

Show that, (1 xx 2^(2) + 2 xx 3^(2) + ….+ n xx (n+1)^(2))/(1^(2) xx 2 + 2^(2) xx 3 + ….+ n^(2) xx (n+1))= (3n+ 5)/(3n+ 1)