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Multiplying different bases with different exponents

  1. May 21, 2016 #1
    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
     
  2. jcsd
  3. May 21, 2016 #2

    Mark44

    Staff: Mentor

    Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
    Is that enough of a hint?
     
  4. May 21, 2016 #3
    Yes. Thank you.
     
  5. May 21, 2016 #4

    Ray Vickson

    User Avatar
    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.
     
  6. May 22, 2016 #5
    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...
     
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