$18^{16n} = 12^{8n} * 9^{12n}$
$(2 * 9)^{16n} = (3 * 4)^{8n} * (3 * 3)^{12n}$
$(2 * 3^2)^{16n} = (3 * 2^2)^{8n} * (3^2)^{12n}$
$2^{16n} * 3^{32n} = 3^{8n} * 2^{16n} * 3^{24n}$
$3^{32n} * 2^{16n} = (3^{8n} * 3^{24n}) * 2^{16n}$
$3^{32n} * 2^{16n} = 3^{8n + 24n} * 2^{16n}$
$3^{32n} * 2^{16n} = 3^{32n} * 2^{16n}$, тождество верно.

$75^{8n} = 225^{4n} * 625^{2n}$
$(3 * 25)^{8n} = (9 * 25)^{4n} * (25^2)^{2n}$
$3^{8n} * 25^{8n} = (3^2 * 25)^{4n} * 25^{4n}$
$3^{8n} * 25^{8n} = 3^{8n} * 25^{4n} * 25^{4n}$
$3^{8n} * 25^{8n} = 3^{8n} * 25^{4n + 4n}$
$3^{8n} * 25^{8n} = 3^{8n} * 25^{8n}$