We report optical measurements demonstrating that the low-energy relaxation rate ($1/tau$) of the conduction electrons in Sr$_2$RuO$_4$ obeys scaling relations for its frequency ($omega$) and temperature ($T$) dependence in accordance with Fermi-liquid theory. In the thermal relaxation regime, $1/taupropto (hbaromega)^2 + (ppikB T)^2$ with $p=2$, and $omega/T$ scaling applies. Many-body electronic structure calculations using dynamical mean-field theory confirm the low-energy Fermi-liquid scaling, and provide quantitative understanding of the deviations from Fermi-liquid behavior at higher energy and temperature. The excess optical spectral weight in this regime provides evidence for strongly dispersing resilient quasiparticle excitations above the Fermi energy.
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