We present a brief description of noncompactified higher-dimensional theories from the perspective general relativity. More concretely, Space-Time-Matter theory, or Induced Matter and reduction procedure used to construct modified Brans-Dicke theory S\'{a}ez-Ballester are briefly explained. Finally, we apply latter Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmological models in arbitrary ...