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We show that $\\chi_c(G^{^{\\frac{2r+1}{2s+1}}})=\\frac{(2s+1)\\chi_c(G)}{(s-r)\\chi_c(G)+2r+1}$ provided that $\\chi_c(G^{^{\\frac{2r+1}{2s+1}}})< 4$. As a consequence, one can see that if ${2r+1 \\over 2s+1} \\leq {\\chi_c(G) \\over 3(\\chi_c(G)-2)}$, then $\\chi_c(G^{^{\\frac{2r+1}{2s+1}}})=\\frac{(2s+1)\\chi_c(G)}{(s-r)\\chi_c(G)+2r+1}$. In particular, $\\chi_c(K_{3n+1}^{^{1\\over3}})={9n+3\\over 3n+2}$ and $K_{3n+1}^{^{1\\over3}}$ has no subgraph with circular chromatic number equal to ${6n+1\\over 2n+1}$. 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