Simple python calculator
For a beginner this is pretty good.
But, there are three glaring problems with it.


You should use a 'main' function.
You should use a dictionary.
operators


Starting with (2), a dictionary holds a key value pair.
If you've come across lists/arrays, it's like them,
apart from that you can use a lot of different types,
not just integers.

Defining one is pretty easy,
and using it will reduce your amount of code.

operators = {
    "+": add,
    "-": sub,
    "*": mul,
    "/": div,
    "pow": pow
}


This will define an object to hold all the operators that you can use.
Now all we need to do is use it.
Using operators.get it's easy.

func = operators.get(operator, None)
if func is None:
    print("Invalid operator!")
    continue


Lovely and simple.

The main function is simple, just move everything in if __name__ == '__main__':
into a function.
With the operator addition you shouldn't really need to make smaller functions,
but it may be a good idea, making a function to get user input, could be a good idea.
But it's up to you.
If you did want to do both of these, you'd do something like:

def main():
    while True:
        number1, number2, operator = get_user_input()
        func = operators.get(operator, None)
        if func is None:
            print("Invalid operator!")
            continue

        print(func(number1, number2))

if __name__ == '__main__':
    main()


Just to note, you may not want to make get_user_input.

Something that you may not know is you can use the builtin operators library.
This will allow you to remove all your definitions of add, sub, etc.
And will allow you to change operators to:

import operator

operators = {
    "+": operator.add,
    "-": operator.sub,
    "*": operator.mul,
    "/": operator.truediv,
    "pow": operator.pow
}


There's some history about Python's division, and that's why it's called truediv, but if you haven't and won't use Python2, then you don't really need to know.