Answer
$\dfrac{125}{3}$
Work Step by Step
We need to apply ratio test for a given series.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} |\dfrac{3^{n+1}}{5^{3(n+1)}} \times \dfrac{5^{3n}}{3^n}|=\dfrac{3}{125}$
This implies that the radius of convergence of the series is $\dfrac{125}{3}$.
