Simplify :
${128}^{\frac{-2}{7}}-({625}^{-3}{)}^{\frac{-1}{4}}+14(2401{)}^{\frac{-1}{4}}$

${128}^{\frac{-2}{7}}-{{625}^{-3}}^{\times \frac{-1}{4}}+14(2401{)}^{\frac{-1}{4}}$

$⟹{2^7}^{\times \frac{-2}{7}}-{{5^{4\times }}^{-3}}^{\times \frac{-1}{4}}+14(7^4{)}^{\frac{-1}{4}}$

$⟹\frac{1}{4}+125+\frac{14}{7}$

$⟹\frac{509}{4}$