PURPOSE: To quantify the variations of the power-law dependences on diffusion time t or gradient frequency f $$ f $$ of extracellular water diffusion measured by diffusion MRI (dMRI). METHODS: Model cellular systems containing only extracellular water were used to investigate the t / f $$ t/f $$ dependence of D ex $$ {D}_{ex} $$ , the extracellular diffusion coefficient. Computer simulations used a randomly packed tissue model with realistic intracellular volume fractions and cell sizes. DMRI measurements were performed on samples consisting of liposomes containing heavy water(D2 O, deuterium oxide) dispersed in regular water (H2 O). D ex $$ {D}_{ex} $$ was obtained over a broad t $$ t $$ range (∼1-1000 ms) and then fit power-law equations D ex ( t ) = D const + const · t - ϑ t $$ {D}_{ex}(t)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {t}^{-{\vartheta}_t} $$ and D ex ( f ) = D const + const · f ϑ f $$ {D}_{ex}(f)={D}_{\mathrm{const}}+\mathrm{const}\cdotp {f}^{\vartheta_f} $$ . RESULTS: Both simulated and experimental results suggest that no single power-law adequately describes the behavior of D ex $$ {D}_{ex} $$ over the range of diffusion times of most interest in practical dMRI. Previous theoretical predictions are accurate over only limited t $$ t $$ ranges; for example, θ t = θ f = - 1 2 $$ {\theta}_t={\theta}_f=-\frac{1}{2} $$ is valid only for short times, whereas θ t = 1 $$ {\theta}_t=1 $$ or θ f = 3 2 $$ {\theta}_f=\frac{3}{2} $$ is valid only for long times but cannot describe other ranges simultaneously. For the specific t $$ t $$ range of 5-70 ms used in typical human dMRI measurements, θ t = θ f = 1 $$ {\theta}_t={\theta}_f=1 $$ matches the data well empirically. CONCLUSION: The optimal power-law fit of extracellular diffusion varies with diffusion time. The dependency obtained at short or long t $$ t $$ limits cannot be applied to typical dMRI measurements in human cancer or liver. It is essential to determine the appropriate diffusion time range when modeling extracellular diffusion in dMRI-based quantitative microstructural imaging.