How did Charlemagne become a rival to the Byzatine
emperors and the Abbasid caliphs?

He proclaimed himself as the Holy Roman Emperor and spread his territory in all directions. While doing that he enter into quarrel with these two countries.

Explanation:

Charlemagne proclaimed himself as an emperor in 800. Until then only rulers of Byzantine Empire had that title in Europe. They didn't accept this, especially as Charlemagne proclaimed himself as the successor of  Roman emperors.

Abbasid caliphs fought with Charlemagne as he tried to take their territory in Spain.

swe hold these truths to be self-evident, that all men are created equal, that they are endowed by their creator with certain unalienable rights, that among these are life, liberty and the pursuit of happiness. — that to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed, — that whenever any form of government becomes destructive of these ends, it is the right of the people to alter or to abolish it, and to institute new government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness. "

- declaration of independence

  according to this passage from the declaration of independence, who gives government the power to exist?

a) the king

b) the people

c) their creator

d) their governmenthook