Tau decays with one charged particle plus multiple<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant="normal">π</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>’s

With the CLEO-II detector at the Cornell Electron Storage Ring, we have measured branching fractions for tau lepton decay into one-prong final states with multiple ${\mathrm{\ensuremath{\pi}}}^{0}$'s ${\mathit{B}}_{\mathit{h}\mathit{n}\mathrm{\ensuremath{\pi}}}^{0}$, normalized to the branching fraction for tau decay into one charged particle and a single ${\mathrm{\ensuremath{\pi}}}^{0}$. We find ${\mathit{B}}_{\mathit{h}2\mathrm{\ensuremath{\pi}}}^{0}$/${\mathit{B}}_{\mathit{h}\mathrm{\ensuremath{\pi}}}^{0}$=0.345\ifmmode\pm\else\textpm\fi{}0.006\ifmmode\pm\else\textpm\fi{}0.016, ${\mathit{B}}_{\mathit{h}3\mathrm{\ensuremath{\pi}}}^{0}$/${\mathit{B}}_{\mathit{h}\mathrm{\ensuremath{\pi}}}^{0}$=0.041 \ifmmode\pm\else\textpm\fi{}0.003\ifmmode\pm\else\textpm\fi{}0.005, and ${\mathit{B}}_{\mathit{h}4\mathrm{\ensuremath{\pi}}}^{0}$/${\mathit{B}}_{\mathit{h}\mathrm{\ensuremath{\pi}}}^{0}$=0.006\ifmmode\pm\else\textpm\fi{}0.002\ifmmode\pm\else\textpm\fi{}0.002.