1. May 21, 2016 #1

   leroyjenkens

   

   1. The problem statement, all variables and given/known data
   Write an expression containing a single radical and simplify.
   
   2. Relevant equations
   [tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]
   
   3. The attempt at a solution
   I can't add the exponents and I can't multiply the bases. I can't take anything out of the radicals to make the bases the same. I have no idea what to do.
   
   Thanks

    

   leroyjenkens, May 21, 2016
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3. May 21, 2016 #2

   Mark44

   

   Insights Author

   Staff: Mentor

   Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
   Is that enough of a hint?

    

   Mark44, May 21, 2016
4. May 21, 2016 #3

   leroyjenkens

   

   Yes. Thank you.

    

   leroyjenkens, May 21, 2016
5. May 21, 2016 #4

   Ray Vickson

   

   Science Advisor

   Homework Helper

   Of course you can combine the bases (just by adding the fractions), and you can even make them the same by putting all fractions over a common denominator.

    

   Ray Vickson, May 21, 2016
6. May 22, 2016 #5

   Nipuna Weerasekara

   

   See the expression as this,
   (xy)^(1/4)*(x^2y)^(1/3)
   then,
   apply power to x and y,
   as follows,
   x^(1/4)*y^(1/4)*x^(2/3)*y^(1/3)
   now remember the rules,
   x^(1/4+2/3)*y^(1/4+1/3)
   now simplify this,
   x^(11/12)*y^(7/12)
   now you might get what to do next...

    

   Nipuna Weerasekara, May 22, 2016

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