When I go to turn my tablet on it frequently powers up. When the screen comes on there is a message: Process system isn't responding. Do you want to close it? Sometimes it will power down when I am still using it. The battery appears to be okay.
Well, it can be a few things that are the cause. I am assuming, by what you wrote, that you turn the device off and on regularly, so restarting it would not be of any help. That is the simplest fix for this. The next option is to change where apps are stored and then restart the device. Meaning if you have any apps stored on and running from an SD card, then moving them back to the tablet and restarting the tablet may resolve the issue.
Should this also not work, then next try a simple "Factory Reset". You can find it in the tablet's "Settings". Just choose the option that lets you keep your personal data. However, a word of caution, doing this without taking the precaution of backing up your personal data (files, contacts, photos, etc., except apps, you can't back those up) to another device or google account could leave you without said items if the reset has any problems.
Should the former type of reset not work, then you are looking at a full "Hard Reset" which will wipe everything and start the tablet like it was when first obtained. The instructions for this are below.
NOTE: Doing this will clear 'all' the data on your tablet, so it is suggested you not choose this option unless you have to, or aren't worried about losing anything on the device.
Be sure you back up any data you want to keep, to a computer or cloud account, before doing the reset.
To "Hard Reset" the tablet...
1. Make sure that the tablet is actually powered off.
2. Remove your SD card, if there is one in the device.
3. Press the "Power" and the "Volume Up" buttons, together, until you see the start-up logo on the screen.
4. Once you can see the logo, release the buttons and allow the device to enter the "System Recovery Mode".
5. Next use "Volume Down" button to get to the "wipe data/factory reset" option.
6. When in recovery mode the "Volume Up" and "Volume Down" buttons are how to can navigate and highlight what option you need.
7. Once you have selected the "wipe data/factory reset", press the "Power" button to select that option.
8. On the following screen, repeatedly press the "Volume Down" button until the "Yes - delete all user data" option is what is selected.
9. Then press the "Power" button to hard reset the tablet.
10. If you took your SD card out in step 2, when the device is up and running again, reinsert the SD card.