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We obtain upper bounds for mixed exponential sums of the type S(x,f,pm) =bx)where pm is a prime power with m ≥ 2 and x is a multiplicative character 2(mod pm). If x is primitive or p( a, b) then we obtain ｜ S(x, f, pm) ｜ ≤2np2-3m. If x is of conductor p