Why is baking powder and baking soda used as leavening instead of yeast?
Not Floyd, but I'll take a shot...
Baking powder's leavening power is both heat and acid activated.
Baking soda's leavening power is acid activated.
The advantage of these is that you can bake right after mixing these with your flour and wet ingredients. This keeps gluten from developing, and you get a very tender, cake-like baked product. Lots of quick breads (like cornbread, cakes, muffins, etc) use this technique to keep crumb tender, when you don't want it chewy or "bread-y".
Yeast takes longer to leaven than either of these (you have to wait for your dough to ferment!), which also results in chewier textures due to the formation of proteins in the dough.
What cranbo said.
I believe baking soda is just a base, whereas baking powder contains both an acid and a base that combine once moisture and heat is added. Ever make a volcano with vinegar and baking soda? That is basically how these two leaven quick breads, with a simple chemical reaction.
Yeast is an organism that feeds on sugars and released cardon dioxide. This process, fermentation, takes considerably longer than an acid/base chemical reaction, but it is worth it because of all the interesting flavors that are released as a result of this process.