Except as otherwise provided in this chapter, it shall be unlawful for any person to practice dentistry or dental surgery or dental hygiene in this state, other than:
1. Those who are now duly licensed dentists, under the laws of this state in force at the time of their licensure; and
2. Those who are now duly licensed dental hygienists under the laws of this state in force at the time of their licensure; and
3. Those who may hereafter be duly licensed as dentists or dental hygienists pursuant to the provisions of this chapter.