Ratio Compounded of 4:9
In a compounded ratio, two or more ratios are multiplied together to form a new ratio. In this case, the compounded ratio of 4:9 means that the two ratios 4:9 are multiplied together to give a new ratio.
To find the compounded ratio of 4:9, we simply multiply the two ratios:
4:9 * 4:9 = 16:81
Therefore, the compounded ratio of 4:9 is 16:81.

Duplicate Ratio of 3:4
The duplicate ratio of a given ratio is obtained by squaring the terms of the ratio. In this case, the duplicate ratio of 3:4 means that each term (3 and 4) is squared to give a new ratio.
To find the duplicate ratio of 3:4, we square each term:
(3)^2 : (4)^2 = 9:16
Therefore, the duplicate ratio of 3:4 is 9:16.

Comparison of Compounded Ratio of 4:9 and Duplicate Ratio of 3:4
Now, let's compare the compounded ratio of 4:9 (16:81) with the duplicate ratio of 3:4 (9:16).
We can see that the compounded ratio of 4:9 (16:81) is not equal to the duplicate ratio of 3:4 (9:16). This shows that the compounded ratio and the duplicate ratio are different concepts and yield different results when calculated.
In conclusion, the compounded ratio of 4:9 is 16:81, while the duplicate ratio of 3:4 is 9:16. Both ratios are obtained through different mathematical operations and result in different values.