for the first, using the ratio test

$L=\displaystyle{\lim_{n\to\infty}}\left |\dfrac{\dfrac{6x^{n+1}}{\sqrt[5]{n+1}}}{\dfrac{6x^n}{\sqrt[5]{n}}}\right |$

$L=\displaystyle{\lim_{n\to\infty}}\left |x \dfrac{\sqrt[5]{n}}{\sqrt[5]{n+1}}\right|$

$L=|x|$

Note also that $L < |x|, \forall n \in \mathbb{N}$

For convergence we must have $L < 1$

so the radius of convergence is

$|x| < 1$

for the second also use the ratio test, the problem is very similar to the first. I leave you to finish the details.