Baking soda is pretty versatile. I wash my face with it, and I bet one could use it in combo with some other natural minerals or oils to make an effective toothpaste.

I've used baking soda and vinegar to replace shampoo and conditioner for three years now, great cost savings and I've finally learned to shave my face after I rinse the vinegar from my hair.

You don't even need "10 simple ingredients" - just use an alum block!