This question already has an answer here:
Now I know what you may be thinking when I pose a question like this, but I do have a reason to wonder.
Work with me for a bit. When did the word "有り難う" come into use, could it have been birthed in the Yamato language? Did it come with the influx of Chinese cultural influence?
This is a question I ask my students in order to get them to think about Japanese objectively. The Portuguese arrived in Japan in 1543. How does one say thank you in Portuguese? Thank you in Portuguese is "obrigado" a slight resemblance with the Japanese expression. Is it a pure coincidence, probably. Could the foriegn influence merely have increased the popularity of "ありがとう" over time? Maybe.
What is an explanation that can disprove a direct relationship between the Portuguese and Japanese expression?