Answer
$\log_6\sqrt[3] {\frac{1}{6}}=-\frac{1}{3}$
Work Step by Step
Use the Power Property. Also, remeber that $\log_aa=1$:
$\log_6\sqrt[3] {\frac{1}{6}}=\log_6\sqrt[3] {6^{-1}}=\log_6(6^{-1})^{\frac{1}{3}}=\log_66^{-\frac{1}{3}}=-\frac{1}{3}\log_66=-\frac{1}{3}(1)=-\frac{1}{3}$
