@Blue Ink: Because it's an outdated mnemonic. Smiley Powers and roots actually should have the same precedence. Apparently it used to be different in the past.

Not that I've ever seen an root without explicit precedence (without the top horizontal line) in the wild, so it's hardly a real problem.

According to the Dutch Wikipedia page on operator precedence, certain math textbooks maintained the old order (with upper line-less roots having lower precedence than multiplication/division) until the end of the 20th century. I guess the textbook that I used did so too, because I definitely remember being taught that mnemonic.