To go into a bit more depth on the RAM, because I love talking about it...
RAM is a piece of hardware that uses the same amount of power, regardless of how much RAM is actually being used by /system/ (the OS and the applications etc..).
Android does a pretty good job at managing its own memory (it used to suck, but has gotten way better over the years, which is why task killers even existed) and will kill tasks as it needs to open new ones (the lag sometimes seen when this happens is usually avoided when the system starts to create cache files, which are placeholders stored to the local disk to be recalled faster when RAM needs it).
So, unused RAM is wasted RAM. Now, there are some cases where heavy power users will actually max out the RAM often, I've never been able to do it, but some claim to. Whatever. This is why a lot of people like to root their phones and disable all the bloat applications on the phone that no one ever uses but the carriers say we have to have. This does in fact free up RAM to make room for the apps you do want to use run slightly faster, though the average user will not really notice.
That's RAM in a very quick nutshell.
What does eat battery: When apps use the CPU, the screen, and the radio (data connection). So, make sure background apps aren't using any of those for better battery performance. Turn off push notifications for instance will help. Tell social apps like Facebook to only refresh when you open the app helps, basically anything that is set to refresh itself in the background on a set schedule is going to use battery.
Hope this helps.
