Compounded ratio is for two given ratios, for example a:b and c : d are two ratios, then their compounded ratio = ac : bd.
Duplicate ratio for a given ratio a : b is a² : b²
Triplicate ratio for a given ratio a : b is a³ : b³
sub-duplicate ratio for a given ratio a : b is √a : √b
sub-triplicate ratio for a given ratio a : b is ∛a : ∛b
Ratio compounded of ratio 4 : 9 with itself will be its duplicate ratio
Duplicate ratio of 3 : 4 is 3² : 4² or 9 :16
Triplicate ratios of 2/3 and 9/7 will be 2³ : 3³ and 9³ : 7³ ,i.e., 8/27 and 729 / 343.
However, if you want to find compounded ratio of 2/3 and 9/7, then it will be (2x9) / (3x7) = 18 / 21 = 6/7