Can anyone please show me how 3^n/6^(2n+1) becomes 1/2^n(6^(n+1))= 1/6)/12^n when you divide top and bottom by 3^n?

Question

Thank you and have a great day!

Answer 1

let's work on the bottom

6^(2n+1)
= 3^(2n+1)* 2^(2n+1)
= 3^n * 3^(n+1) * 2^n * 2^(n+1)
= 3^n * 2^n * 6^(n+1)

now the 3^n would cancel the 3^n on top, leaving you with
1/(2^n * 6^(n+1) )