Washu's lab is actually a subspace dimension that includes five planets. She built it long before she met Tenchi, and changed his closet's door to open into the dimension when she moved in. Isn't she a genius?
The Galaxy Police Academy, Washu's alma mater, is an independent and mysterious organization originally founded by the Jurai for research purposes. Their facilities include an entire solar system, and new technologies developed there are sold to underwrite their classes. The academy releases the most powerful inventions only to the Galaxy Police and the armed forces of Jurai.