SOLUTION: ^3√16x^4y^3 times ^3√12x^2y^4

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Question 178163: ^3√16x^4y^3 times ^3√12x^2y^4
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C16x%5E4y%5E3%29%2Aroot%283%2C12x%5E2y%5E4%29 Start with the given expression


root%283%2C16x%5E4y%5E3%2A12x%5E2y%5E4%29 Combine the radicals


root%283%2C192x%5E6y%5E7%29 Multiply


root%283%2C64%2A3%2Ax%5E3%2Ax%5E3%2Ay%5E3%2Ay%5E3%2Ay%29 Factor each term where at least one term is a perfect cube.


root%283%2C64%29%2Aroot%283%2C3%29%2Aroot%283%2Cx%5E3%29%2Aroot%283%2Cx%5E3%29%2Aroot%283%2Cy%5E3%29%2Aroot%283%2Cy%5E3%29%2Aroot%283%2Cy%29 Break up the cube root.


4%2Aroot%283%2C3%29%2Ax%2Ax%2Ay%2Ay%2Aroot%283%2Cy%29 Take the cube root of 64 to get 4. Take the cube root of x%5E3 to get "x". Take the cube root of y%5E3 to get "y".


4x%5E2%2Ay%5E2%2Aroot%283%2C3y%29 Rearrange the terms and multiply.


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Answer:


So root%283%2C16x%5E4y%5E3%29%2Aroot%283%2C12x%5E2y%5E4%29=4x%5E2%2Ay%5E2%2Aroot%283%2C3y%29