Hi Zach,
He says (I couldn't find the datasheet) that the TDA7000 works with a supply voltage from 2.0V (worn-out two alkaline cells), to 10V which is a brand new 9V alkaline battery.
Have you ever seen the small size of the cells inside a 9V battery? They surely won't last long. Compare the size (and spec's) of those tiny cells with AAA or AA cells. Two AA cells aren't much bigger than a 9V battery but will last at least 6 times longer, and are cheaper. Your choice.
I don't like 9V batteries anymore, I'm designing thingys for 3V now.
Have you seen this one?:
https://www.electronics-lab.com/projects/science/018/index.html