Can someone help me simplify this radical expression?

[rogermiranda]

I have the cube root of 15 divided by the cube root of 10.
First I simplified the fraction to the cube root of 3 divided by the cube root of 2. Then if I rationalize the denominator I am left with the cube root of 6 divided by the cube root of 4. The answer seems to be the cube root of 12 divided by 2.
But I am not sure on how to simplify this expression. Please help!

[nona.m.nona]

The process for "rationalizing" the square-root denominators was to create a situation in which you doubled (by multiplying by another copy of) whatever factors remained inside the radical, since square roots required squares in order to simplify.

The process for cube-root denominators has the same philosophy. But cube roots to not require squares in order to simplify. What do they need instead? So do you need to double the factors, or do something else?

For an explanation and examples, try this page.

[rogermiranda]

Thank you for your help! I now understand on how to get the correct answer.