(2^(n+2) * 21^(n+3))/(6^n+1)*7^(n+2))

Question

(2^(n+2) * 21^(n+3))/(6^n+1)*7^(n+2))

Answer 1

2 ^( N + 2 ) = 2 ^ N * 2 ^ 2 
====================
21 ^ ( N + 3 ) = 7 ^ ( N + 3 ) * 3 ^ ( N + 3 ) = 7^N * 3^N * 7^3 * 3^ 3 
==================================================
6^ (N+1) = 2 ^(N+1) * 3^(N + 1) = 2^N * 2 * 3^N * 3 
==================================================
7^(N+2) = 7^N * 7^2 
=================================================
( 2^N * 2^2 * 7^N * 3^N * 7^3 * 3^3 ) / ( 2^N * 2 * 3^N * 3 * 7^N * 7^2 ) =
= ( 2 * 7 * 3^2 ) = 14 * 9 = 126