Anomalously high values of power α (1.6 < α < 12) are found in power laws in conductance versus energy relationships in carbon-nanotube peapod quantum dots, encapsulating a chain of C60 molecules. This power is controllable by the applied back gate voltage. Atomic-like behaviors with doubly degenerate ground states are also found by single electron spectroscopy. They reveal that a portion of power originates from the Tomonaga-Luttinger liquid via the occupied electronic levels, which originate from the subbands unique to the peapods. This observation also clarify that the encapsulated C60 molecules do not directly contribute to the above quantum phenomena in peapods.