Let $\alpha>0,\ \beta>0$ be such that $\alpha^3+\beta^2=4$. If the maximum value of the term independent of $x$ in the binomial expansion of $\left(\alpha x^{1/9}+\beta x^{-1/6}\right)^{10}$ is $10k$, then $k$ is equal to :

(1) $176$

(2) $336$

(3) $352$

(4) $84$

(1) $176$

(2) $336$

(3) $352$

(4) $84$