Question

find the ones digit in the numbers 3^89 and 8^89

Answer 1

Write out the powers of 3 until the 1's digit repeats: 3^1=3, 3^2=9, 3^3=27, 3^4=81, 3^5=243, 3^6=729, etc. The cycle repeats after 4.

From that, we can conclude that if the remainder when the power is divided by 4 is 1, the one's digit will be 3 (3^1, 3^5, etc.) If the remainder is 2, the one's digit should be 9 (3^2, 3^6, etc.) Complete the the pattern, and you can get the answer.

Answer 2

Interesting factoid: 8^89 is about 2.4 times the number of atoms in the visible universe