Topic, The topic where you can only post the most random things you can think of that doesn't make sense...

85^10=19,687,440,434,072,265,625

With a huge computation like this, I break it down into different parts. I noted that 85^10=(85^5)^2=(85^4*85)^2=((85^2)^2*85)^2, then computed 85^2 as 7,225.

The method I used for squaring each of these bigger numbers is to break it down into two sections. In general you can let N=A*10^n+B and then compute N^2 as (A^2*10^2n+B^2)+2*A*B*10^n, which are easier calculations to perform in my opinion.

85^4=7,225^2=(7,200^2+25^2)+7,200*50=51,840,625+360,000=52,200,625

85^5=52,200,625*85=4,437,053,125

4,437,053,125^2=((44,370)^2*10^10+(53,125)^2)+2*44,370*53125*10^5

44,370^2=100*4,437^2=100*((44^2*10,000+37^2)+2*44*37*100)=100*((19,361,369)+(325,600))=1,968,696,900

53,125^2=(53^2*10^6+125^2)+2*53*125*10^3=(2,809,015,625)+13,250,000=2,822,265,625

2*44,370*53,125=44,370*106,250=4,437,000,000+266,220,000+8,874,000+2,218,500=4,714,312,500

Finally:

85^10=4,437,053,125^2=(1,968,696,900*10^10+2,822,265,625)+4,714,312,500*10^5=(19,686,969,002,822,265,625)+471,431,250,000,000=19,687,440,434,072,265,625

In case you want to check that you have the right answer, it's n(n+1)/2. The point of the question isn't to give the answer, it's to explain how you got to it.