L = { e, 0, 0000, 000000000}.
L* = ( e + 0 + 0000 + 000000000)*
= ( e + 0 + 0000 + 000000000)( e + 0 + 0000 + 000000000)( e + 0 + 0000 + 000000000)….
= (e, 0, 00, 000, 0000, 00000,…….) {use e and 0 from each grouping to generate this}
= 0*
Hence L is an RL.
Note: (Shorter and faster way to solve the sum as mentioned by @raja11sep)
Every finite language is regular.
Regular languages are closed under Kleene closure.