Answer
$\displaystyle \frac{x^{5}}{3y^{3}}$
Work Step by Step
We use the Properties of Exponents, step by step...
P0. $a^{0}=1,\ a^{1}=a$
P1. $a^{m}\cdot a^{n}=a^{m+n}$
P2. $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$ , $ \displaystyle \frac{1}{a^{n}}=a^{-n}$
P3. $(a^{m})^{n}=a^{mn}$
P4. $(ab)^{m}=a^{m} b^{m}$
P5. $(\displaystyle \frac{a}{b})^{m}=\frac{a^{m}}{b^{m}}$
P6. Rational exponents: $a^{m/n}=(a^{1/n})^{m}\sqrt[n]{a^{m}}$
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$\displaystyle \frac{3^{-1}\cdot x\cdot y^{2}}{x^{-4}y^{5}}=3^{-1}\cdot\frac{x^{1}}{x^{-4}}\cdot\frac{y^{2}}{y^{5}}$= ... P$2$...
$=3^{-1}\cdot x^{1-(-4)}\cdot y^{2-5}$
$=3^{-1}\cdot x^{5}\cdot y^{-3}$= ... P$2$...$= \displaystyle \frac{x^{5}}{3y^{3}}$
