< b="" /> Solution: < />

< b="" /> Understanding the given ratio: < />

- The given ratio is x : y = 3 : 4
- This means that x is 3 parts and y is 4 parts.

< b="" /> Finding the values of x and y: < />

- Let's assume x = 3k and y = 4k, where k is a constant.
- Therefore, x = 3k and y = 4k.

< b="" /> Calculating the values of x², y², and xy: < />

- x² = (3k)² = 9k²
- y² = (4k)² = 16k²
- xy = (3k)(4k) = 12k²

< b="" /> Calculating the values of x²y, xy², x³, and y³: < />

- x²y = x² * y = 9k² * 4k = 36k³
- xy² = x * y² = 3k * 16k² = 48k³
- x³ = (3k)³ = 27k³
- y³ = (4k)³ = 64k³

< b="" /> Final Ratio: < />

- Therefore, the ratio x²y : xy² : x³ : y³ is 36k³ : 48k³ : 27k³ : 64k³
- Simplifying the ratio, we get 9 : 12 : 6 : 16

Thus, the final ratio of x²y : xy² : x³ : y³ is 9 : 12 : 6 : 16.