4. The sum $b_{8}^{2}+b_{9}^{2}+\ldots+b_{2020}^{2}$ of the squares of the terms of the geometric progression $\left\{b_{n}\right\}, b_{n}>0$ is 4. The sum of their reciprocals $\frac{1}{b_{8}^{2}}+\frac{1}{b_{9}^{2}}+\ldots+\frac{1}{b_{2020}^{2}}$ is 1. Find the product $b_{8}^{2} \cdot b_{9}^{2} \cdot \ldots \cdot b_{2020}^{2}$.
Answer: $b_{8}^{2} \cdot b_{9}^{2} \cdot \ldots \cdot b_{2020}^{2}=2^{2013}$.