Michelle Obama: Hey Beyonce, This is How I Do You!

Michelle Obama nailed Beyonce ... with chops and mannerisms!

The First Lady joined 'Late Late Show' host James Corden for "Carpool Karaoke" and rocked Bey's "Single Ladies." Check out the vid ... Michelle did Stevie Wonder justice too ... and Missy Elliott also joined the ride along.

It wasn't all fun and games ... the First Lady also got her message out about education.