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Let $P_n^t$ denote the $t$-th power of a monotone path on $n$ vertices. The ordered Ramsey numbers of powers of paths have been extensively studied. We prove that there exists an absolute constant $C$ such that $R_<(K_s,P_n^t)\\leq R(K_s,K_t)^{C} \\cdot n$ holds for all $s,t,n$, which is tight up to the value of $C$. 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Let $P_n^t$ denote the $t$-th power of a monotone path on $n$ vertices. The ordered Ramsey numbers of powers of paths have been extensively studied. We prove that there exists an absolute constant $C$ such that $R_<(K_s,P_n^t)\\leq R(K_s,K_t)^{C} \\cdot n$ holds for all $s,t,n$, which is tight up to the value of $C$. 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