Here's the completed code using recursion:
```python
def raise_to_power(base_val, exponent_val):
if exponent_val == 0:
result_val = 1
else:
result_val = base_val * raise_to_power(base_val, exponent_val - 1)
return result_val
user_base = int(input())
user_exponent = int(input())
print('{}^{} = {}'.format(user_base, user_exponent, raise_to_power(user_base, user_exponent)))
```
In the function `raise_to_power()`, we use recursion to multiply the `base_val` by itself `exponent_val` times, until `exponent_val` reaches 0. At that point, we return 1, because any number raised to the power of 0 equals 1.
When `exponent_val` is not 0, we use the formula `base_val * raise_to_power(base_val, exponent_val - 1)` to calculate the result recursively. This means we multiply the base value by the result of the function called with the same base and an exponent of `exponent_val - 1`.
Finally, we print out the result using string formatting.