Answer :

AL2006
That would become (XY)^4/3 . The exponent is still rational. Sorry.
[tex]\left(x^4y^4\right)^\frac{1}{3}=x^{4\cdot\frac{1}{3}}y^{4\cdot\frac{1}{3}}=x^\frac{4}{3}y^\frac{4}{3}=x^{1\frac{1}{3}}y^{1\frac{1}{3}}=x^{1+\frac{1}{3}}y^{1+\frac{1}{3}}=x^1x^\frac{1}{3}y^1y^\frac{1}{3}\\\\=x\sqrt[3]{x}\cdot y\sqrt[3]y=xy\sqrt[3]{xy}[/tex]