Answer
$\dfrac{x^{\frac{3}{4}}y^{\frac{1}{6}}}{xy}$
Work Step by Step
When one exponential term is divided by another exponential term with the same base, subtract the exponents, keeping the base as-is:
$\left(x^{\frac{1}{2} - \frac{3}{4}}\right) \cdot \left(y^{-\frac{1}{3} - \frac{1}{2}}\right)$
Before subtracting the fractional exponents, convert fractions such that they have the same denominator:
$\left(x^{\frac{2}{4} - \frac{3}{4}}\right) \cdot \left(y^{-\frac{2}{6} - \frac{3}{6}}\right)$
Subtract the exponents:
$x^{-\frac{1}{4}} \cdot y^{-\frac{5}{6}}$
Get rid of negative exponents by moving the exponential term to the denominator, changing the exponent from negative to positive:
$\dfrac{1}{x^{\frac{1}{4}} \cdot y^{\frac{5}{6}}}$
Do not leave fractional exponents in the denominator. To get rid of negative exponents in the denominator, multiply both numerator and denominator by a factor that will make the denominator have non-fractional exponents. In this case, the factors will be $x^{\frac{3}{4}}$ and $y^{\frac{1}{6}}$:
$\dfrac{x^{\frac{3}{4}} \cdot y^{\frac{1}{6}}}{x^{\frac{1}{4}} \cdot y^{\frac{5}{6}} \cdot x^{\frac{3}{4}}\cdot y^{\frac{1}{6}}}$
When one exponential term is multiplied with another exponential term with the same base, add the exponents, keeping the base as-is:
$\dfrac{x^{\frac{3}{4}}y^{\frac{1}{6}}}{x^{\frac{4}{4}} y^{\frac{6}{6}}}$
Simplify fractional exponents:
$\dfrac{x^{\frac{3}{4}}y^{\frac{1}{6}}}{xy}$
