**Solution:**

Given, the ratio of x to y is 3:4.

Let's assume the value of x as 3k and the value of y as 4k, where k is a constant.

Therefore, we can write x = 3k and y = 4k.

**Finding the value of x^2y:**

To find the value of x^2y, we substitute the values of x and y into the expression.

x^2y = (3k)^2 * (4k) = 9k^2 * 4k = 36k^3

**Finding the value of xy^2:**

To find the value of xy^2, we substitute the values of x and y into the expression.

xy^2 = (3k) * (4k)^2 = 3k * 16k^2 = 48k^3

**Finding the value of x^3y^3:**

To find the value of x^3y^3, we substitute the values of x and y into the expression.

x^3y^3 = (3k)^3 * (4k)^3 = 27k^3 * 64k^3 = 1728k^6

**Simplifying the expression:**

Now, we can simplify the expression x^2y + xy^2 - x^3y^3.

x^2y + xy^2 - x^3y^3 = 36k^3 + 48k^3 - 1728k^6

Combining like terms, we get:

84k^3 - 1728k^6

Therefore, the value of x^2y + xy^2 - x^3y^3 is 84k^3 - 1728k^6.

Since the value of k is not given, we cannot determine the exact numerical value of the expression. However, we can simplify it further if required.

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