strager's blag

Yesterday, our math teacher announced there was to be held a county-sponsored math competition the following day. Long story short, I had a day to prepare for the competition. Sadly, I didn't know what to prepare for until the following day (that is, the day of the test). I was given a sample test and worked those math problems.

One of the problems was of the following sort:

Give the first 4 digits of 2009²⁰⁰⁹.

This is a crazy problem, and I was sure there was some stupid math trick which wasn't really math to accomplish this.