If \( \frac{x}{y}=\frac{1}{9} \) and \( \frac{y}{z}=\frac{9}{8} \), then \( \frac{z}{x}=? \)

To solve for \( \frac{z}{x} \), we start with the given ratios: 1. \( \frac{x}{y} = \frac{1}{9} \) implies that \( x = \frac{y}{9} \). 2. \( \frac{y}{z} = \frac{9}{8} \) implies that \( y = \frac{9}{8}z \). Now we have expressions for \( x \) and \( y \) in terms of \( z \). Substituting \( y \) from the second equation into the first equation: Substituting \( y \) into \( x = \frac{y}{9} \): \[ x = \frac{\frac{9}{8}z}{9} = \frac{z}{8}. \] Now we can find \( \frac{z}{x} \): \[ \frac{z}{x} = \frac{z}{\frac{z}{8}} = 8. \] Thus, the final answer is: \[ \frac{z}{x} = 8. \]