$1,2,2,4,8,32,256,\ldots,$each term (starting from the third term) is the product of the two terms before it. for example, the seventh term is $256$, which is the product of the fifth term ($8$) and the sixth term ($32$). this sequence can be continued forever, though the numbers very quickly grow enormous! (for example, the $14^{\text{th}}$ term is close to some estimates of the number of particles in the observable universe.) what is the last digit of the $35^{\text{th}}$ term of the sequence?
