How to get black burned on food off copper bottom of pan?

I have tried baking soda and ketchup. Don't want to scratch. Other than outside bottom, it's like new. Do you have a different suggestion? Has anyone tried oven cleaner?
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Elbow Grease & Comet on my stainless/copper bottom Revereware pots & pans and a green scrubber sponge doesn't hurt them,if my daughter burns something on them I put pan/pot bottom in big bowl or deep plate and just soak in water before scrubbing or put wet paper towel with dawn on them for awhile. It'll turn copper dark(dishwasher will too) but then I use comet or clay cleaner to clean off & shine them up they look like new after. The clay cleaner is called BioCleaner I use this on my Glass stove top,Stainless sinks,pots & pans & appliances,shower door,faucets it cleans shines,protects. It's the best ever. The clay cleaner won't scratch if your worried about that. Don't use the oven cleaner.
Thanks Lynn, I'll stay away from the oven cleaner. I have used the comet and well, elbow grease for days. The burnt areas are a thin black crust...won't budge! I know there is shiny copper under there!
Put the pan with the bottom into a second larger pan. Filk the lower Pam with water and a cup of vinegar and boil for 30 minutes. Then use the copper cleaner. It should come off