Final answer:
To divide the given expression, simplify it and then cancel out common factors.
Step-by-step explanation:
To divide the given expression, (4y)/(3x)-:(2y^(4))/(9xy), we can simplify it first. Dividing by a fraction is the same as multiplying by its reciprocal. We can rewrite the expression as (4y)/(3x) * (9xy)/(2y^(4)). Now, we can simplify by canceling out common factors.
First, we can simplify (4y)/(2y^(4)) as 2/y^(3).
Next, we can cancel out common factors in the numerator and denominator. Canceling out y in 9y and 3y, and x in 9x and 3x, our final expression is (2/y^(3)) * (3/1) = 6/y^(3).
The simplified form of the expression is 6/y^(3).
Learn more about Division of rational expressions