#### Answer

$\dfrac {1}{3}\log _{4}a+\dfrac {1}{4}\log _{4}b-\dfrac {1}{2}\log _{4}c-\dfrac {2}{3}\log _{4}d$

#### Work Step by Step

$\log _{4}\dfrac {\sqrt [3] {a}\times \sqrt [4] {b}}{\sqrt {c}\sqrt [3] {d^{2}}}=\log _{4}\left( a^{\dfrac {1}{3}}b^{\dfrac {1}{4}}c^{-\dfrac {1}{2}}d^{-\dfrac {2}{3}}\right) =\dfrac {1}{3}\log _{4}a+\dfrac {1}{4}\log _{4}b-\dfrac {1}{2}\log _{4}c-\dfrac {2}{3}\log _{4}d$