  We have studied the in- and out-of-plane magnetic penetration depths in the
hole- doped iron based superconductor Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$
($T_{c}\approx$ 30K). The study was performed on single crystals grown from
different fluxes and we find that the results are nearly the same. The in-plane
London penetration depth $\lambda_{ab}$ does not show exponential saturation at
low temperature, as would be expected from a fully gapped superconductor.
Instead, $\lambda_{ab}(T)$ shows a power-law behavior, $\lambda\propto T^{n}$
($n\approx 2$), down to $T\approx 0.02 T_{c}$, similar to the electron doped
Ba(Fe$_{1-x}$Co$_{x}$)$_{2}$As$_{2}$. The penetration depth anisotropy
$\gamma_{\lambda}=\lambda_{c}(T)/\lambda_{ab}(T)$ increases upon cooling,
opposite to the trend observed in the anisotropy of the upper critical field,
$\gamma_{\xi}=H_{c2}^{\perp c}(0)/H_{c2}^{\parallel c}(0)$. These are universal
characteristics of both the electron and hole doped 122 systems, suggesting
unconventional superconductivity. The behavior of the in-plane superfluid
density $\rho_{ab}(T)$ is discussed in light of existing theoretical models
proposed for the iron pnictides superconductors.
