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Math·Advanced Math·Equivalent expressions

hard

$$\sqrt{(4y{)}^3}=8{\left(\sqrt[9]{y}\right)}^k$$
In the given equation, $y>0$, and $k$ is a constant. What is the value of $k$?

A

$\frac{2}{9}$

B

$\frac{2}{27}$

C

$\frac{27}{2}$

D

27