Multiplying different bases with different exponents

  • #1
575
47

Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

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
 

Answers and Replies

  • #2
34,695
6,399

Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

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
Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
Is that enough of a hint?
 
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Likes Nipuna Weerasekara and leroyjenkens
  • #3
575
47
Hint: ##\sqrt[4]{x^3} = \sqrt[12]{x^9}##
Is that enough of a hint?
Yes. Thank you.
 
  • #4
Ray Vickson
Science Advisor
Homework Helper
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Homework Statement


Write an expression containing a single radical and simplify.

Homework Equations


[tex]\sqrt[4]{xy}\sqrt[3]{x^2{y}}[/tex]

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
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.
 
  • Like
Likes Nipuna Weerasekara
  • #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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