The first tap selection is Honolulu from Honolulu, where Eleanor does a tap dance to hula music.

Arguably the best dancing put on film, Fred Astaire and Eleanor Powell mastered Begin the Beguine in Broadway Melody of 1940 even doing different variations of dance to the same song. Here's another section of Begin the Beguine. I've Got My Eyes On You is the number Fred Astaire, George Murphy, and of course Eleanor Powell did as the finale to this film.

From Broadway Melody of 1936, Eleanor does a dance without music. From the same film, Everybody Sing. 

When Eleanor Powell made appearances on Broadway, she did sing on her own (she was dubbed in her films). Here are a few samples from At Home Abroad from 1935. The first is Got a Bran' New Suit. One of the most charming numbers from the show is That's Not Cricket. The final song is What a Wonderful World.