How do I simplify cubed roots with multiple variables and coefficients?

[AnTiFreeze3]

Homework Statement

Simplify...

Homework Equations

Starting Equation:

³√9xy^4 * ³√12x³y

The Attempt at a Solution

(Sorry ahead of time if this is sloppy)

³√9xy^4 * ³√12x³y - I broke up each part of the cubed roots to try and simplify them³√9 * ³√x * ³√y * ³√y³ * ³√y * ³√12 * ³√x³ * ³√y³ - I then simplified the obvious cubed roots, and simplified √12 to 2√3:

y * ³√9xy * 2x * ³√3y - This is where I'm stuck.I don't understand how I can simplify if further when 9 has no rational number that can be multiplied by itself 3 times to get to 9, yet apparently the answer to it doesn't have 9 under the radical.

The answer, to help out anybody who wants to help me, is:

3xy * ³√4xy²Thanks for any help.

 

[ehild]

What is really under the roots? Use parentheses! Bring everything under a single cubic root. ehild

 

[AnTiFreeze3]

What is really under the roots? Use parentheses! Bring everything under a single cubic root. ehild

Alright, thanks for the help. So, since I have a coefficient and similar variables under the cubed roots, I can change around where they all go?

And at first, I thought ehild was trying to call me a child for not knowing the answer, and just misspelled it...