```
def powers(L):
    '''
    (list of ints) -> bool
    Return True if the given list of ints is a list of powers of some
    int x of the form [x^0, x^1, x^2, x^3, ...] and False otherwise.
    >>>powers[1, 3, 9, 27, 81]
    True
    '''
    i = 1
    x = L[0]
    while i < len(L):
        if L[i] == x**(i+1):
            i += 1
            return True
        else:
            return False

```

I have changed the mistakes you have pointed out for me, but it still doesn't work.. Can you please help me with it?