SOLUTION: Simplify {{{root(5,320x^17y^15)}}}

Algebra ->  Radicals -> SOLUTION: Simplify {{{root(5,320x^17y^15)}}}      Log On


   

Question 126396: Simplify

root%285%2C320x%5E17y%5E15%29
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%285%2C320x%5E17y%5E15%29 Start with the given expression


root%285%2C320%29%2Aroot%285%2Cx%5E17%29%2Aroot%285%2Cy%5E15%29 Break up the root



2%2Aroot%285%2C10%29%2Aroot%285%2Cx%5E17%29%2Aroot%285%2Cy%5E15%29 Simplify root%285%2C320%29 to get 2%2Aroot%285%2C10%29


2%2Aroot%285%2C10%29%2Ax%5E3%2Aroot%285%2Cx%5E2%29%2Aroot%285%2Cy%5E15%29 Simplify root%285%2Cx%5E17%29 to get x%5E3%2Aroot%285%2Cx%5E2%29


2%2Aroot%285%2C10%29%2Ax%5E3%2Aroot%285%2Cx%5E2%29%2Ay%5E3 Simplify root%285%2Cy%5E15%29 to get y%5E3


2x%5E3y%5E3%2Aroot%285%2C10x%5E2%29 Combine the roots and multiply


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So root%285%2C320x%5E17y%5E15%29 simplifies to 2x%5E3y%5E3%2Aroot%285%2C10x%5E2%29



In other words, root%285%2C320x%5E17y%5E15%29=2x%5E3y%5E3%2Aroot%285%2C10x%5E2%29