This is the adverb of homogeneous. You use it when something is mixed, spread, grouped, or made so that every part is of the same type. Dye that is homogeneously mixed does not leave darker patches. A population that is homogeneously spread is not bunched in one corner of the map. Teachers talk about grouping students homogeneously — putting similar levels together — which some people like and some people fight. It is a stiff, laboratory-sounding word; in speech "evenly" or "all in the same way" will usually do the job. Keep the adjective's stress and add -ly: ho-muh-JEE-nee-us-lee. Do not rush it into ho-MOJ-en-us-lee; that squash belongs more to homogenize.