As a continuation of Part I, vague integral powers of elements in vague groups and their representation properties are introduced in this paper. Thereafter, some rudimentary algebraic properties of vague integral powers of elements, obtained from the generalized vague associative law formulated in Part I, are established. The present paper particularly provides the abstract foundations of integral powers and multiples of real numbers in vague arithmetic. For this reason, special attention is also paid to the calculation of integral powers and multiples of real numbers in vague arithmetic, and some practical applications related to the discrete structure of measurement instruments are also given. (C) 2005 Elsevier Inc. All rights reserved.