  In this paper we further develop the method of quaternion typification of
Clifford algebra elements suggested by the author in the previous paper. On the
basis of new classification of Clifford algebra elements it is possible to
reveal and prove a number of new properties of Clifford algebra. We use k-fold
commutators and anticommutators. In this paper we consider Clifford and
exterior degrees and elementary functions of Clifford algebra elements.
