  We are concerned with the inviscid limit of the Navier-Stokes equations to
the Euler equations for barotropic compressible fluids in $\mathbb{R}^3$. When
the viscosity coefficients obey a lower power-law of the density (i.e.,
$\rho^\delta$ with $0<\delta<1$), we identify a quasi-symmetric
hyperbolic--singular elliptic coupled structure of the Navier-Stokes equations
to control the behavior of the velocity of the fluids near the vacuum. Then
this structure is employed to prove that there exists a unique regular solution
to the corresponding Cauchy problem with arbitrarily large initial data and
far-field vacuum, whose life span is uniformly positive in the vanishing
viscosity limit. Some uniform estimates on both the local sound speed and the
velocity in $H^3(\mathbb{R}^3)$ with respect to the viscosity coefficients are
also obtained, which lead to the strong convergence of the regular solutions of
the Navier-Stokes equations with finite mass and energy to the corresponding
regular solutions of the Euler equations in $L^{\infty}([0, T]; H^{s}_{\rm
loc}(\mathbb{R}^3))$ for any $s\in [2, 3)$. As a consequence, we show that, for
both viscous and inviscid flows, it is impossible that the $L^\infty$ norm of
any global regular solution with vacuum decays to zero asymptotically, as $t$
tends to infinity. Our framework developed here is applicable to the same
problem for the other physical dimensions via some minor modifications.
