jmc

The common ratio between consecutive terms is $\frac{3}{5}$ (you can choose any two consecutive terms and divide the second one by the first to find the common ratio). So the $n^{\text{th}}$ term of the sequence is $\frac{125}{9}\cdot {\left(\frac{3}{5}\right)}^{n-1}$. Plugging in $n=8$, we get $$\frac{125}{9}\cdot {\left(\frac{3}{5}\right)}^7=\frac{5^3}{3^2}\cdot \frac{3^7}{5^7}=\frac{3^5}{5^4}=\boxed{\frac{243}{625}}.$$