If an applicant for the dental examination or an applicant for the dental hygienist examination fails to make the required average grade as specified by the board, he may make an application to the board for reexamination on a form to be furnished by the board on request and he may take a new examination or examinations at such time and place as is specified by the board, upon payment by an applicant of a reexamination fee equivalent to the dentist examination fee or upon payment by an applicant for examination as a dental hygienist of a reexamination fee equivalent to the dental hygienist examination fee. The new examination or examinations and subsequent registration, if any, shall be governed by the provisions of sections 332.151 and 332.251, respectively.