Rationalize the denominator. Assume that all expressions under radicals represent positive numbers.

The square root of 3y^4 to the third root divided by the square root of 15x^4 to the third root.
Here is what I have so far:
I multiplied. The square root of 100x^2 to the third root divided by the square root of 100x^2 to the third root= the square root of 300x^2y^4 to the third root divided by 10x^2.
Now I'm not sure what to do because I keep getting the wrong answer.
Thanks for the help.

To rationalize the denominator, you need to eliminate the square root from the denominator. Here's how you can proceed:

1. Begin with the expression: (sqrt(3y^4)^(1/3)) / (sqrt(15x^4)^(1/3))

2. Simplify the radicals individually by applying the power rule:
sqrt(3y^4)^(1/3) = (3y^4)^(1/6) = (3^(1/6))(y^4)^(1/6) = (3^(1/6))(y)^(4/6) = (3^(1/6))(y^(2/3))

sqrt(15x^4)^(1/3) = (15x^4)^(1/6) = (15^(1/6))(x^4)^(1/6) = (15^(1/6))(x)^(4/6) = (15^(1/6))(x^(2/3))

3. Now, rewrite the expression with the simplified radicals:
(3^(1/6))(y^(2/3)) / (15^(1/6))(x^(2/3))

4. To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator. The conjugate of (15^(1/6))(x^(2/3)) is (15^(1/6))/((x^(2/3)).

Therefore, the expression becomes:
[(3^(1/6))(y^(2/3))] * [(15^(1/6))/(x^(2/3))] / [(15^(1/6))/((x^(2/3))]

5. Now simplify the expression by canceling out common factors:
(3^(1/6))(y^(2/3))(15^(1/6))(x^(2/3)) / (15^(1/6))(x^(2/3))
= (3^(1/6))(y^(2/3))

Thus, the rationalized denominator of the given expression is (3^(1/6))(y^(2/3)).