algebra 2 help?

Question

what is the answer to this problem?

x to the 1/2 times y to the 1/3

is it x to the 3/6 and y to the 2/6
or do you combine the exponents and then its (xy) to the 5/6

i know if it were x to 3/6 times x to the 2/6 you add the exponents but idk what to do when there are two different variables

this is the only thing im confused on. thanks for the help

Answer 1

x^(1/2) = x^(3/6)
y^(1/3) = y^(2/6), so you can write them as
(x³y²)^(1/6)

Answer 2

If you have two different variables, or bases, then you don't need to do anything. x to the 1/2 times y to the 1/3 remains
x^(1/2) * y^(1/3).

Answer 3

you can do as you were trying to do getting a common root which as you stated is 6

so you would have the sixth root (x^3*y^2)