Multiplying different bases with different exponents

[leroyjenkens]

Homework Statement

Write an expression containing a single radical and simplify.

Homework Equations

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

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

 

[Mark44]

Homework Statement

Write an expression containing a single radical and simplify.

Homework Equations

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

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?

 

[leroyjenkens]

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

Yes. Thank you.

 

[Ray Vickson]

Homework Statement

Write an expression containing a single radical and simplify.

Homework Equations

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

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.

 

[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...