SOLUTION: for positive real numbers x,y,z, what is the equivalent to x^1/2 y^2/3 z^5/6? a. 3 sqrt xy^2 z^3 b. 6 sqrt xy^2 z^5 c. 6 sqrt x^3 y^2 z^5 d. 6 sqrt x^3 y^4 z^5 e. 11

Algebra ->  Radicals -> SOLUTION: for positive real numbers x,y,z, what is the equivalent to x^1/2 y^2/3 z^5/6? a. 3 sqrt xy^2 z^3 b. 6 sqrt xy^2 z^5 c. 6 sqrt x^3 y^2 z^5 d. 6 sqrt x^3 y^4 z^5 e. 11      Log On


   

Question 254892: for positive real numbers x,y,z, what is the equivalent to x^1/2 y^2/3 z^5/6?
a. 3 sqrt xy^2 z^3
b. 6 sqrt xy^2 z^5
c. 6 sqrt x^3 y^2 z^5
d. 6 sqrt x^3 y^4 z^5
e. 11 sqrt xy^2 z^5
i guessed d. b/c i multiplied 6*3 =18, then i put 18/6 = 1/2 ...but i need help please am i doing this all wrong?
Found 2 solutions by richwmiller, jim_thompson5910:
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
You are cute.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Take note that the LCD of the denominators in the exponents is 6. So you can rewrite each fraction with a denominator of 6. So for 1%2F2, multiply it by 3%2F3 to get 3%2F6. Likewise, multiply 2%2F3 by 2%2F2 to get 4%2F6.


So the expression x%5E%281%2F2%29y%5E%282%2F3%29z%5E%285%2F6%29%5E%22%22 then can be rewritten as x%5E%283%2F6%29y%5E%284%2F6%29z%5E%285%2F6%29%5E%22%22


Now use the identity x%5E%28yz%29=%28x%5Ey%29%5Ez to convert x%5E%283%2F6%29y%5E%284%2F6%29z%5E%285%2F6%29%5E%22%22 into %28x%5E3y%5E4z%5E5%29%5E%281%2F6%29.


Finally, convert to radical notation to get root%286%2Cx%5E3y%5E4z%5E5%29


So x%5E%281%2F2%29y%5E%282%2F3%29z%5E%285%2F6%29%5E%22%22=root%286%2Cx%5E3y%5E4z%5E5%29 where every variable is non-negative.