SOLUTION: I'd like to know how to simplify the following: {{{The 3rd SQRT of 80x to the 17th power/The 3rd SQRT of 9yz to the 6th}}} I'm not sure if I should eliminate the square root by pu

Algebra ->  Square-cubic-other-roots -> SOLUTION: I'd like to know how to simplify the following: {{{The 3rd SQRT of 80x to the 17th power/The 3rd SQRT of 9yz to the 6th}}} I'm not sure if I should eliminate the square root by pu      Log On


   

Question 191863: I'd like to know how to simplify the following:
The+3rd+SQRT+of+80x+to+the+17th+power%2FThe+3rd+SQRT+of+9yz+to+the+6th I'm not sure if I should eliminate the square root by putting parentheses around the entire expression and cubing it, or if I should pull x to the 5th out, leaving the problem as x to the 5th * the 3rd sqrt of 80x squared. And the same problem with the denominator...do I pull out z squared, leaving me with z squared * the 3rd sqrt of 9y. Or do I go with my first instinct and cube everything...leaving me with 512,000 x to the 51st/729 y3z18? Yikes. Any help would be greatly appreciated. Thanks in advance!
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
%28%2880x%5E17%29%5E%281%2F3%29%29%2F%28%289yz%5E%286%29%29%5E%281%2F3%29%29
I think by "3rd sqrt" you mean cube root.
I don't know a cube root symbol here, so I used exponent of 1/3.
= %28%28%2880x%5E17%29%29%2F%28%289yz%5E%286%29%29%29%29%5E%281%2F3%29
= 2x%5E5%2A%28%28%2810x%5E2%29%29%2F%28%289yz%5E%286%29%29%29%29%5E%281%2F3%29
= %282x%5E5%2Fz%5E2%29%2A%28%28%2810x%5E2%29%29%2F%28%289y%29%29%29%5E%281%2F3%29