Let α>0, β>0 be such that α^3+β^2=4. If the maximum value of the term independent of x in the binomial expansion of (α x^(1/9)+β x^-1/6)^10 is 10 k,…

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