Answer
$\frac{1}{3}$
Work Step by Step
$\ln \sqrt[3] e$ can be rewritten as $\ln e^{\frac{1}{3}}$.
$\ln e^{\frac{1}{3}}$ is in the form $\ln e^x$, and $\ln e^x = x$, thus $\ln e^{\frac{1}{3}} = \frac{1}{3}$.
This is because $\ln e^x$ can be rewritten as $\log_e e^x$, and $e$ must be raised to the power of $x$ to become $e^x$.