IKMC 2027 - Grades 11-12 - Self-study SET 10 - Thematic Batch 3 Question 8

For positive real numbers a, b, define $x_{1}$=a, $y_{1}$=b, $x_{n+1}$=a$\sqrt{y_n}$ and $y_{n+1}$=b$\sqrt{x_n}$. The ratio $x_{5}$/$y_{5}$ can be written as $(a/b)^{m}$. What is m?