1. **State the problem:** Given the equation $z = \frac{e^y}{x}$, we want to understand or manipulate this expression. 2. **Formula and rules:** The expression involves the exponential function $e^y$ divided by $x$. Important rules: - Exponential function $e^y$ means $e$ raised to the power $y$. - Division by $x$ means the entire exponential term is divided by $x$. 3. **Intermediate work:** The expression is already simplified as $z = \frac{e^y}{x}$. 4. **Explanation:** This formula shows that $z$ depends on both $x$ and $y$. For a fixed $y$, as $x$ increases, $z$ decreases because of division. For a fixed $x$, as $y$ increases, $z$ increases exponentially. 5. **Summary:** The function $z = \frac{e^y}{x}$ describes how $z$ changes with $x$ and $y$ using exponential growth in the numerator and linear division in the denominator.