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= 2^(3n+2) *50^(3n+2) *3^(2n+1) *8^(2n+1)/ 4^2n *8^2n *50^(2n+2) *3^2n* 5^2n=
= 2^3n *2^2 *2^n *5^2n *50^2 *3 *8 / 2^4n *2^2 *5^4 * 5^2n=
=2^2 *50^2 *5^2n *3*2 / 2^n * 5^4= 6*2^2 *50^2 *5^2n/ 625* 2^n=
= 24*2500*5^2n / 625*2^n= 96*5^2n / 2^n

100^(3n+2) * 24^(2n+1) / [32^(2n) * 50^(2n+2) * 15^(2n)] =

__ 100^(3n+2) = 100^(3n) * 100^(2) = 100^(2) * 100^(n) * 100^(2n)
__ 24^(2n+1) = 24^(2n) * 24 = 8^(2n) * 3^(2n) * 24
__ 32^(2n) = 8^(2n) * 4^(2n)
__ 50^(2n+1) = 50^(2n) * 50^(1) = 50 * 50^(2n)
__ 15^(2n) = 5^(2n) * 3^(2n)
=>
= 100^(2) * 100^(n) * 100^(2n) * 8^(2n) * 3^(2n) * 24 / [8^(2n) * 4^(2n) *
* 50^(2) * 50^(2n) * 5^(2n) * 3^(2n)] =

= (100/50)^2 * 24 * 100^(n) * [100^(2n) * 8^(2n) * 3^(2n) / 8^(2n) * 4^(2n)
* 50^(2n) * 5^(2n) * 3^(2n)] =

= 2^(2) * 24 * 100^(n) * [(100/50)^n * (8/8)^n * (3/3)^(2n) / 4^(2n) * 5^(2n)] =

= 96 * 100^n * [2^n * 1 * 1 / 4^(2n) * 5^(2n)] =

= 96 * 200^n / 20^(2n) =
= 96 * 20^n * 10^n / (20^n * 20^n) =
= 96 * (20/20)^n * (10/20)^n =
= 96 * 1 * (1/2)^n = 96 / 2^(n)

=96