1. **State the problem:** We want to find the limit as $q \to 1$ of the expression $$\lim_{q \to 1} \left( \frac{q^n}{n-1} - \frac{1}{\ln n^n} \right)^?$$ where the exponent is not specified, so we assume the limit expression inside the parentheses. 2. **Rewrite and analyze the expression:** The expression inside the limit is $$\frac{q^n}{n-1} - \frac{1}{\ln n^n}.$$ Note that $$\ln n^n = n \ln n.$$ So the expression becomes $$\frac{q^n}{n-1} - \frac{1}{n \ln n}.$$ 3. **Consider the behavior as $q \to 1$:** When $q \to 1$, $q^n \to 1^n = 1$. So the expression tends to $$\frac{1}{n-1} - \frac{1}{n \ln n}.$$ 4. **Check for any indeterminate forms:** The expression depends on $n$, which is not specified to tend to any value. If $n$ is fixed and $n \neq 1$, the limit is simply $$\frac{1}{n-1} - \frac{1}{n \ln n}.$$ 5. **If $n$ is fixed and $n \neq 1$, the limit is:** $$\boxed{\frac{1}{n-1} - \frac{1}{n \ln n}}.$$ 6. **If $n$ tends to 1 or another value, more information is needed.** --- **Regarding the second part:** Given $z = (1 + c)^p$, this is a general exponential expression where $c$ and $p$ are constants or variables. No further question was asked about this. --- **Summary:** The limit as $q \to 1$ of $$\frac{q^n}{n-1} - \frac{1}{\ln n^n}$$ is $$\frac{1}{n-1} - \frac{1}{n \ln n}$$ assuming $n$ is fixed and $n \neq 1$.