SOLUTION: simplify by taking roots of the numerator and the denominator.Assume all expressions under the radicals represent positive numbers. cubed rt of 512x^5/y^3 please help....

Algebra ->  Radicals -> SOLUTION: simplify by taking roots of the numerator and the denominator.Assume all expressions under the radicals represent positive numbers. cubed rt of 512x^5/y^3 please help....      Log On


   

Question 264531: simplify by taking roots of the numerator and the denominator.Assume all expressions under the radicals represent positive numbers.
cubed rt of 512x^5/y^3
please help....
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
root%283%2C%28512x%5E5%29%2F%28y%5E3%29%29 Start with the given expression.


root%283%2C512x%5E5%29%2Froot%283%2Cy%5E3%29 Break up the root.


root%283%2C8%5E3x%5E5%29%2Froot%283%2Cy%5E3%29 Rewrite 512 as 8%5E3 (since 512=8%5E3)


root%283%2C8%5E3x%5E3x%5E2%29%2Froot%283%2Cy%5E3%29 Rewrite x%5E5 as x%5E3x%5E2 (since x%5E5=x%5E3x%5E2)


root%283%2C8%5E3%29root%283%2Cx%5E3%29root%283%2Cx%5E2%29%2Froot%283%2Cy%5E3%29 Break up the root in the numerator.


%288%2Aroot%283%2Cx%5E3%29root%283%2Cx%5E2%29%29%2Froot%283%2Cy%5E3%29 Evaluate the cube root 8%5E3 to get 8. Remember the cube root of anything cubed is simply that original expression. In other words, root%283%2Cx%5E3%29=x. This is why everything was broken down into parts dealing with cubes.


%288x%2Aroot%283%2Cx%5E2%29%29%2Froot%283%2Cy%5E3%29 Evaluate the cube root x%5E3 to get 'x'.


%288x%2Aroot%283%2Cx%5E2%29%29%2Fy Evaluate the cube root y%5E3 to get 'y'.


So root%283%2C%28512x%5E5%29%2F%28y%5E3%29%29=%288x%2Aroot%283%2Cx%5E2%29%29%2Fy where y%3C%3E0