Answer
$\ln{\left(\frac{ac^{\frac{1}{3}}}{b^2}\right)}$
Work Step by Step
Recall:
(1) $n\cdot \ln{a}=\ln{a^n}$
(2) $\ln{a}+\ln{b}=\ln{(ab)}$
(3) $\ln{a}-\ln{b} = \ln{\left(\frac{a}{b}\right)}$
Use rule (1) above to obtain:
\begin{align*}
&=\ln{a}-\ln{(b^2)}+\ln{\left(c^{\frac{1}{3}}\right)}
\end{align*}
Use rule (3) above to obtain:
\begin{align*}
&=\ln{\left(\frac{a}{b^2}\right)}+\ln{\left(c^{\frac{1}{3}}\right)}
\end{align*}
Use rule (2) above to obtain:
\begin{align*}
&=\ln{\left(\frac{a}{b^2} \cdot c^{\frac{1}{3}}\right)}\\\\
&=\ln{\left(\frac{ac^{\frac{1}{3}}}{b^2}\right)}
\end{align*}