What considerations are there when using powdered or pasteurized eggs in baking cake?
Pasteurized liquid eggs should work 1:1 as a substitute for whole eggs.  Obviously, at this point, you cannot separate the yolks and whites, so you cannot use them for recipes which require separation.  You would use approximately 1/4 cup of pasteurized egg per large egg in the original recipe.

Similarly, you can use reconstituted powdered egg, although the flavor may not be the same.   I wouldn't do this in a yellow cake whose flavor is dependent on eggs, but in a chocolate cookie, it might be perfectly acceptable.  Again, reconstitute the powder first according to its directions, so it is liquid, and then use about 1/4 cup per large egg from the original recipe.