The powers conferred by this part upon counties not having adopted a home rule charter shall not be exercised within the boundaries of a municipality within said county unless the governing body of the municipality expresses its consent by resolution. Such a resolution consenting to the exercise of the powers conferred upon counties by this part shall specifically enumerate the powers to be exercised by the county within the boundaries of the municipality. Any power not specifically enumerated in such a resolution of consent shall be exercised exclusively by the municipality within its boundaries.