Write a Python function `nth_power(nums, n)` that takes a list of numbers `nums` and an integer `n`, and returns a new list where each number in `nums` is raised to the power of `n`.
#### Example Usage
```python [main.nopy]
print(nth_power([1, 2, 3, 4], 2)) # Output: [1, 4, 9, 16]
print(nth_power([2, 3, 4], 3)) # Output: [8, 27, 64]
print(nth_power([5, 10], 0)) # Output: [1, 1]
```
#### Constraints
- The input list `nums` will contain integers.
- The integer `n` can be positive, negative, or zero.