Answer
$\dfrac{x^{2}}{3y^{2}}$
Restriction: $x \ne 0$; $y \ne 0$
Work Step by Step
Let's first take a look at the problem to see what we can cancel out from the numerator and denominator:
$\dfrac{5x^3y}{15xy^3}$
We can divide the numerator and denominator by $5$:
$\dfrac{x^3y}{3xy^3}$
When we divide exponents with the same base, we keep the base as-is and subtract the exponents. Let's rewrite to reflect this:
$\dfrac{1}{3}(x^{3 - 1})(y^{1 - 3})$
Subtract the exponents:
$\dfrac{1}{3}(x^{2})(y^{-2})$
We don't want to leave negative exponents, so we need to convert them to positive exponents by taking their reciprocals and switching the sign of the exponents:
$\dfrac{x^{2}}{3y^{2}}$
To find out if there are any restrictions on the variables, we need to find which values of $x$ and/or $y$ will cause the denominator to equal zero, which would make the whole expression undefined. To state the restrictions, we set the denominator of the fraction equal to zero and see which values of $x$ and $y$ will make the denominator zero.
Restriction: $x \ne 0$; $y \ne 0$
