Which is the correct simplified form of the expression x^1/2y^-1/3/x^1/4y^1/2

[tex]\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ [/tex]

[tex]\bf \cfrac{x^{\frac{1}{2}}y^{-\frac{1}{3}}}{x^{\frac{1}{4}}y^{\frac{1}{2}}}\implies \cfrac{x^{\frac{1}{2}}x^{-\frac{1}{4}}}{y^{\frac{1}{2}}y^{\frac{1}{3}}}\implies \cfrac{x^{\frac{1}{2}-\frac{1}{4}}}{y^{\frac{1}{2}+\frac{1}{3}}}\implies \cfrac{x^{\frac{2-1}{4}}}{y^{\frac{3+2}{6}}}\implies \cfrac{x^{\frac{1}{4}}}{y^{\frac{5}{6}}}[/tex]