Answer
$\dfrac {2}{3}$
Work Step by Step
$x=\log _{4}\sqrt [3] {16}\Rightarrow 4^{x}=\sqrt [3] {16}\Rightarrow 4^{x}=\sqrt [3] {4^{2}}\Rightarrow 4^{x}=4^{\dfrac {2}{3}}\Rightarrow x=\dfrac {2}{3}$
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