Reposition dates in a random filename

I am trying to rename family photos and all of the names are completely random. I managed to rename the dates in the file names so they follow the patterns: "(yyyy-mm-dd)_" and "(yyyy-mm)_" respectively. The date patterns are scattered in random positions in my filenames and I want to move them to the front of my filenames. I think I can define my date patterns as "(*)_" , but I'm not sure how to move it. Is this possible?

See the User Guide:
www.advancedrenamer.com/user_guide/regular_expresions

Parentheses have special meanings in regular expressions so will need to be "escaped" in order to represent themselves - ie \( and \(.

Use parentheses to capture the prefix and date strings and reverse the order:

Replace: ^(.*)(\(.*\)_)
With: \2\1

Reply to #2:
Thank you so much for the reply!! I really appreciate the explantation, your solution worked great and helped me figure out a few other tricks. I don't think I would have figured out how to escape the parentheses without going in circles for a few hours. Lol.