Question

How did the Jews religion survive through the exile of the jews

Answer 1

They worshipped together during the Sabbath and in synagogues. 

Answer 2

Jews have remained a people despite exile and dispersion. In all of human history, there have been less than ten exiles of an entire people out of their country. It’s a highly unusual phenomenon to take a whole people and throw them out of their country.

Multiple exiles are unheard of, since after the first one the people generally disappear—they simply become assimilated among other peoples. In human history, multiple exiles and dispersion are unique only to the Jewish people.

The dispersion of the Jewish People to the four corners of the globe is a completely unique phenomenon in human history. Jews have wandered and settled in almost every land on earth -while somehow managing to maintain their distinct national identity.

http://www.simpletoremember.com/articles/a/7-wonders-of-jewish-history/

and yea. their faith and strength in their Jewish faith probably played a really big part in maintaining the religion.