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In this paper we compute the Waring rank of any polynomial of the formF=M_1+...+M_r, where the M_i are pairwise coprime monomials, i.e.,GCD(M_i,M_j)=1 for i not j. In particular, we determine the Waring rank of anymonomial. As an application we show that certain monomials in three variablesgive examples of forms of rank higher than the generic form. As a furtherapplication we produce a sum of power decomposition for any form which is thesum of pairwise coprime monomials.

The Waring rank of the sum of pairwise coprime monomials