If functional programmers try python...

fixedpoints.py

fix = lambda f: lambda a: \
    f(fix(f))(a)

power = lambda x: lambda n: \
    fix(lambda g: lambda n: 1 if n == 0 else x * g(n-1))(n)
factorial = lambda n: \
    fix(lambda g: lambda n: 1 if n == 0 else n * g(n-1))(n)

power(3)(4)
# 3^4 = 81

factorial(5)
# 5! = 120