Answer
$log_{4}(\sqrt[3] \frac{x}{y})$
Work Step by Step
Based on the quotient rule of logarithms, we know that $log_{b}(\frac{M}{N})=log_{b}M-log_{b}N$ (where $b$, $M$, and $N$ are positive real numbers and $b\ne1$).
Therefore, $\frac{1}{3}(log_{4}(x)-log_{4}(y))=\frac{1}{3}log_{4}(\frac{x}{y})$.
According to the power rule of logarithms, we know that $log_{b}M^{p}=plog_{b}M$ (when $b$ and $M$ are positive real numbers, $b\ne1$, and $p$ is any real number).
Therefore, $\frac{1}{3}log_{4}(\frac{x}{y})=log_{4}(\sqrt[3] \frac{x}{y})$.