Solution:

Given, x:y = 3:4

Let us assume that x = 3a and y = 4a (where a is a constant)

Hence, x2y = (3a)2 (4a) = 36a3

Also, xy2 = (3a) (4a)2 = 48a3

And, x3 y3 = (3a)3 (4a)3 = 1728a6

Therefore, x2y:xy2:x3 y3 = 36a3:48a3:1728a6

On simplifying, we get:

x2y:xy2:x3 y3 = 3:4:144

Hence, the value of x2y:xy2:x3 y3 is 3:4:144.

Explanation:

To solve the given problem, we need to use the concept of ratios and solve for the values of x2y, xy2, and x3 y3.

We assume that x and y are in the ratio of 3:4. By doing so, we can easily represent x and y in terms of a constant, say a. This helps us to find the values of x2y, xy2, and x3 y3.

We use the formulae x2y = x^2 * y, xy2 = x * y^2, and x3 y3 = x^3 * y^3 to find the values of x2y, xy2, and x3 y3 respectively.

Finally, we simplify the ratio by dividing each term by the highest common factor, which is 12a3. This gives us the required ratio of x2y:xy2:x3 y3 as 3:4:144.