Is there a way of multiplying a polynomial in X &Y with fractional powers with another such polynomial to get polynomial in X &Y with integer powers?

Question

I want to take something like $X^{m/k}+X^{(m-1)/k}+Y^{1/k}$ and multiply it by another polynomial in $X^{1/k}$ and $Y^{1/k}$ to get a polynomial without fractional powers, ideally irreducible in $K[x,y]$, $K$ a finite field. Is that possible in general? Is there a general procedure to find such a polynomial?

Thanks in advance!