High-intensity, extreme-ultraviolet (XUV) femtosecond interactions with large rare-gas clusters of xenon and argon have been studied at a wavelength of 38 nm. Pulses of XUV radiation with nJ energy are produced by high-order harmonic conversion from a 35-fs, near-infrared, terawatt laser. Mass resolved ion spectra show charge states up to Xe${}^{8+}$ and Ar${}^{4+}$. Kinetic-energy measurements of ions and electrons indicate that a nanoplasma is formed and a hydrodynamic cluster explosion ensues after heating by the short wavelength pulse. It appears that the observed charge states and electron temperatures are consistent with sequential, single-photon ionization and collisional ionization of ions that have had their ionization potential depressed by plasma continuum lowering in the cluster nanoplasma.