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

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) (Show Source): You can put this solution on YOUR website!
You are cute.
Answer by jim_thompson5910(35256) (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 , multiply it by to get . Likewise, multiply by to get .

So the expression then can be rewritten as

Now use the identity to convert into .

Finally, convert to radical notation to get

So where every variable is non-negative.
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