It was between a smaller under-equipped mexican army and the world power of

I think the "it" is the Battle of Puebla, 5th May 1862, right?
The world power at the time was France, which was especially strong militarily, and was seen as one of the strongest armies at the time.

Social and economicthe concept of international social responsibility is the expectation that mncs concern themselves about social and economic effects of their decisions regarding activities in other countries.