# Multiplying different bases with different exponents

1. May 21, 2016

### leroyjenkens

1. The problem statement, all variables and given/known data
Write an expression containing a single radical and simplify.

2. Relevant equations
$$\sqrt[4]{xy}\sqrt[3]{x^2{y}}$$

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. May 21, 2016

### Staff: Mentor

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

3. May 21, 2016

### leroyjenkens

Yes. Thank you.

4. May 21, 2016

### Ray Vickson

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.

5. May 22, 2016

### 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...