8.1. Given positive numbers $a, b, c, d, e$. It is known that $a b=2, b c=3, c d=4, d e=15$, $e a=10$. What is the value of $a$?
Answer: $a=\frac{4}{3}$.

Multiply the first, third, and fifth equations and divide by the second and fourth: $\frac{a b \cdot c d \cdot e a}{b c \cdot d e}=\frac{2 \cdot 4 \cdot 10}{3 \cdot 15}$. From this, $a^{2}=\frac{16}{9}$ and $a=\frac{4}{3}$.