Final answer:
The Portuguese established trading posts in various parts of Asia, but not in Laos. Laos became part of French Indochina, and thus was not an area where the Portuguese had established a trading outpost. Burma was a British colony and also not under Portuguese trade influence.
Step-by-step explanation:
In the context of Southeast Asian history, the Portuguese were able to establish trading posts in several places but not in others. During their global exploration and trade expansion, the Portuguese focused largely on securing coastal ports and trade routes which helped them control the lucrative spice trade. When considering the establishment of Portuguese trading outposts in Asia, it is significant to note the extent of regional control and influence exerted by various colonial powers.
Specifically, Laos was not a part of the Portuguese trading network. It became part of the area known as French Indochina after France reinforced its influence in Asia. Other areas mentioned, such as Vietnam (their coastal trading influence), Ayuthaya, and Thailand (formerly Siam), were influenced by the Portuguese to varying degrees. Burma, on the other hand, was a British colony and was not an area where the Portuguese established a trading post. Therefore, out of the given options, Laos is the correct answer as it was not a location where the Portuguese established trading outposts.
Thai and French influences in the region, as well as British dominance over Burma, further reinforce why Laos and Burma were not under Portuguese trading influence, whereas other locations were.