Answer
$x^{1/6}y^{1/4}$
Work Step by Step
Use the rule $\frac{a^m}{a^n}=a^{m-n}$ to obtain:
$\dfrac{x^{2/3}y^{-1/4}}{x^{1/2}y^{-1/2}}=x^{2/3 - 1/2}\cdot y^{-1/4 - (-1/2)}=x^{2/3 - 1/2}\cdot y^{-1/4+1/2}$
Before we subtract the exponents, because they are in fraction form, we need to convert these fractions so their denominators are the same:
The least common denominator for the exponents for $x$ is $6$. The least common denominator for the exponents for $y$ is $4$. Let us convert the fractions accordingly, then simplify:
$=x^{4/6 - 3/6}y^{-1/4 +2/4}$
$=x^{1/6}y^{1/4}$
