Question about Remainders and Exponents Video

I had a quick question about your video for ‘Remainders and Exponents’. When finding the unit digit for 33^33, you look at the pattern for 3^32, referring to 32, saying that it is a multiple of 4 and then come to the conclusion that the unit digit of 33^33 would be 3, since that would follow 33^32’s unit digit of 1.

My question is, why can’t you use the 3^33 off the bat by saying that 33 is a multiple of 3 and use the unit digit of 7 (I’m aware this is incorrect). But, just wondering what logic is used and how. Trying to see if I’m missing something.

It’s finding a pattern on 3^x, 3^{x + 1}, 3^{x + 2} and so on. So it depends on the size of the x, x + 1, x + 2, … sequence till you get a pattern, not 3 itself.