1. Let's clarify your problem: you want to understand the expression involving the power of $\tan \frac{x}{y}$ and why it might be wrong or misinterpreted. 2. The function $\tan \frac{x}{y}$ means you take the tangent of the fraction $\frac{x}{y}$, not $\tan x$ divided by $y$. 3. If you write something like $(\tan x)^y$ (power on tangent), it is different from $\tan \frac{x}{y}$. 4. Common mistakes happen if you misread or miswrite: for example, $\tan \frac{x}{y} \neq \frac{\tan x}{y}$. 5. Always use parentheses clearly to indicate powers or arguments, for example: - $\left(\tan \frac{x}{y}\right)^n$ means the tangent of $\frac{x}{y}$ raised to the power $n$. - $\tan \left(\frac{x}{y}\right)$ means tangent of $\frac{x}{y}$. 6. So, if your expression is $\tan \frac{x}{y}$ raised to some power, write it as $\left(\tan \frac{x}{y}\right)^p$ to avoid confusion. 7. In summary, check parentheses and the placement of the power to ensure the expression is written and interpreted correctly.