Answer
$x=16$
Work Step by Step
RECALL:
$\log_b{a}=y \longrightarrow b^y=a$
With $a=x$, $b=64$, and $y=\frac{2}{3}$, use the rule above to the given expression to obtain:
$64^{\frac{2}{3}}=x$
Use the rule $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$ to obtain:
$(\sqrt[3]{64})^2=x
\\(\sqrt[3]{4^3})^2=x$
Use the rule $\sqrt[3]{a^3} = a$ to obtain:
$4^2=x
\\4(4)=x
\\16=x$