Answer
$64^{\frac{1}{6}}=\sqrt[6] 64=2$
Work Step by Step
For all positive numbers $a$, where $a\ne1$, and all positive numbers $x$, we know that $y=log_{a}x$ means the same as $x=a^{y}$.
Therefore, $log_{64}2=\frac{1}{6}$ means the same as $64^{\frac{1}{6}}=\sqrt[6] 64=2$.