Answer:
[tex]\frac{x^\frac{1}{4}}{y^\frac{5}{6}}[/tex]
Step-by-step explanation:
[tex]\frac{x^\frac{1}{2}y^\frac{-1}{3}}{x^\frac{1}{4}y^\frac{1}{2}}[/tex]
To simplify the exponent we apply exponential property
[tex]\frac{a^m}{a^n} =a^{m-n}[/tex]
[tex]\frac{x^\frac{1}{2}}{x^\frac{1}{4}}=x^{\frac{1}{2} -\frac{1}{4}}=x^\frac{1}{4}[/tex]
[tex]\frac{y^\frac{-1}{3}}{y^\frac{1}{2}}=x^{\frac{-1}{3} -\frac{1}{2}}=x^-\frac{5}{6}[/tex]
[tex]x^\frac{1}{4} y^-\frac{5}{6}[/tex]
[tex]\frac{x^\frac{1}{4}}{y^\frac{5}{6}}[/tex]
