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Observation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn><mml:mo stretchy="false">(</mml:mo><mml:mo>+</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msubsup><mml:mrow><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:mi>S</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msubsup><mml:msup><mml:mrow><mml:mi>π</mml…
By analyzing an ${e}^{+}{e}^{\ensuremath{-}}$ data sample corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ taken at a center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the branching fractions of the Cabibbo-favored hadronic decays ${D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\eta}}^{\ensuremath{'}}$, ${D}^{0}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{0}{\ensuremath{\eta}}^{\ensuremath{'}}$, and ${D}^{+}\ensuremath{\rightarrow}{K}_{S}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\eta}}^{\ensuremath{'}}$, which are determined to be $(6.43\ifmmode\pm\else\textpm\fi{}0.1{5}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.3{1}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, $(2.52\ifmmode\pm\else\textpm\fi{}0.2{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.1{5}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and $(1.90\ifmmode\pm\else\textpm\fi{}0.1{7}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}0.1{3}_{\mathrm{syst}})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, …