SOLUTION: Use rational exponents to write x^1/5*y^1/3*z^1/6 as a single radical expression. I come up with ^120 sqrt x^18y^30z^15, however, this is not one of the options for an answer.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use rational exponents to write x^1/5*y^1/3*z^1/6 as a single radical expression. I come up with ^120 sqrt x^18y^30z^15, however, this is not one of the options for an answer.       Log On


   

Question 352213: Use rational exponents to write x^1/5*y^1/3*z^1/6 as a single radical expression.
I come up with ^120 sqrt x^18y^30z^15, however, this is not one of the options for an answer.
Am I to simplify?
Answer options are
A. ^90 sqrt xyz
B. ^30 sqrt xyz
C. ^30 sqrt (xyz)^21
D. ^30 sqrt x^6y^10z^5
Any help is greatly appreciated! Thank you in advance for your time and help!
Found 2 solutions by Fombitz, jim_thompson5910:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find a common denominator using 5,3, and 6.
LCD=30
1%2F5=6%2F30+
1%2F3=10%2F30
1%2F6=5%2F30
x%5E%281%2F5%29%2Ay%5E%281%2F3%29%2Az%5E%281%2F6%29=%28x%5E6y%5E10z%5E5%29%5E%281%2F30%29
x%5E%281%2F5%29%2Ay%5E%281%2F3%29%2Az%5E%281%2F6%29=root%2830%2C%28x%5E6y%5E10z%5E5%29%29

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E%281%2F5%29%2Ay%5E%281%2F3%29%2Az%5E%281%2F6%29%5E%22%22 Start with the given expression.


Take note that the LCD is 30. So let's get each fraction to have a denominator of 30.


x%5E%286%2F30%29%2Ay%5E%281%2F3%29%2Az%5E%281%2F6%29%5E%22%22 Multiply the first fraction by 6%2F6


x%5E%286%2F30%29%2Ay%5E%2810%2F30%29%2Az%5E%281%2F6%29%5E%22%22 Multiply the second fraction by 10%2F10


x%5E%286%2F30%29%2Ay%5E%2810%2F30%29%2Az%5E%285%2F30%29%5E%22%22 Multiply the third fraction by 5%2F5


%28x%5E6y%5E10z%5E5%29%5E%281%2F30%29%5E%22%22 Factor out the denominator.


root%2830%2Cx%5E6y%5E10z%5E5%29 Convert to radical notation.


So the answer is D)