Answer: ask the web; it knows everything. And it says "inside a 9-volt battery".
I slipped a letter opener under the bottom edge of a new 9-volt battery where the metal meets the cardboard and lifted up a corner. Then, with a pair of pliars, I peeled off the cover. Here's what I found:
The batteries are held together with a bit of blue shrink-wrap, which I sliced off:
Now they come apart like an accordian. They're held together with spot-welded straps.
By gently pulling them apart, each battery came off with one or two bits of joining strip; gently pulling THAT off with a pair of pliers gave me 6 batteries and some scrap.
After lightly filing off the sharp corner left by pulling off the welded strap, I had 6 AAAA batteries for about $2.
:)