Exact Quantization of Even-Denominator Fractional Quantum Hall State at $\nu$=5/2 Landau Level Filling Factor

We report ultra-low temperature experiments on the obscure fractional quantum Hall effect (FQHE) at Landau level filling factor $\nu$=5/2 in a very high mobility specimen of $\mu =1.7\times {10}^7$ cm${}^2$/Vs. We achieve an electron temperature as low as $\sim$ 4~mK, where we observe vanishing $R_{xx}$ and, for the first time, a quantized Hall resistance, $R_{xy}=h\mathrm{/}(5\mathrm{/}2e^2)$ to within 2 ppm. $R_{xy}$ at the neighboring odd-denominator states $\nu$=7/3 and 8/3 is also quantized. The temperature dependences of the $R_{xx}$-minima at these fractional fillings yield activation energy gaps ${\mathrm{\Delta }}_{5\mathrm{/}2}$=0.11K, ${\mathrm{\Delta }}_{7\mathrm{/}3}$=0.10K, and ${\mathrm{\Delta }}_{8\mathrm{/}3}$=0.055K.