2y^2*3xy^3 divided by 3x^2y^4

To divide the expression 2y^2 * 3xy^3 by 3x^2y^4, you need to follow these steps:

Step 1: Distribute the product of 2y^2 and 3xy^3 to each term in the denominator, which is 3x^2y^4.

(2y^2 * 3xy^3) / (3x^2y^4)

Step 2: Multiply the coefficients together:

2 * 3 = 6

Step 3: Multiply the variables with the same bases together.

For "y" in the numerator and denominator: y^2 * y^3 = y^(2+3) = y^5
For "x" in the numerator and denominator: x * x^2 = x^(1+2) = x^3

Step 4: Divide the numerator and denominator by the common factors.

In this case, both the numerator and the denominator have a factor of "y^4" and "3x".

(y^5 / y^4) becomes y^(5-4) = y^1 = y
(6x^3) / (3x) simplifies to 2x^2.

Putting it all together, the expression simplifies to:

2x^2y / y^4