SOLUTION: Can you please help me solve this problem? (3 times the fourth root of x^3y)+(5 times the fourth root of x^7y^5)

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Question 190602: Can you please help me solve this problem? (3 times the fourth root of x^3y)+(5 times the fourth root of x^7y^5)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Aroot%284%2Cx%5E3y%29%2B5%2Aroot%284%2Cx%5E7y%5E5%29 Start with the given expression.


3%2Aroot%284%2Cx%5E3y%29%2B5%2Aroot%284%2Cx%5E4%2Ax%5E3y%5E4%2Ay%29 Factor x%5E7y%5E5 to get x%5E4%2Ax%5E3y%5E4%2Ay


Break up the root.


3%2Aroot%284%2Cx%5E3y%29%2B5%2Ax%2Aroot%284%2Cx%5E3%29%2Ay%2Aroot%284%2Cy%29 Take the 4th root of x%5E4 and y%5E4 to get "x" and "y"


3%2Aroot%284%2Cx%5E3y%29%2B5xy%2Aroot%284%2Cx%5E3y%29 Recombine the roots.


%283%2B5xy%29%2Aroot%284%2Cx%5E3y%29 Factor out the GCF root%284%2Cx%5E3y%29


So 3%2Aroot%284%2Cx%5E3y%29%2B5%2Aroot%284%2Cx%5E7y%5E5%29=%283%2B5xy%29%2Aroot%284%2Cx%5E3y%29 where every variable is non-negative.