Find the term independent o f x in the expansion of the following expressions: `(1/2 x^(1/3)+x^(-1/5))^8`

Explanation

Suppose the `(r+1)` th term in the given expansion is independent of `x`.


Thus, we have:


`T_{r+1}=\ ^{8} C_{r}(frac{1}{2} x^{1 / 3})^{8-r}(x^{-1 / 5})^{r} `


`=\ ^{8} C_{r} frac{1}{2^{8-r}} x^{frac{8 r}{3}}-frac{r}{5}`


...