find the last digit in 3^9999.
I doubt you can find it!!
http://www51.wolframalpha.com/input/?i=3^9999
To find the last digit of a number raised to a power, we can look for a pattern by calculating the last digit of smaller powers of that number. Let's start by examining the last digit of powers of 3:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
3^7 = 2187
3^8 = 6561
3^9 = 19683
You can observe that the last digit repeats after every 4th power: 3, 9, 7, 1. Therefore, to find the last digit of 3^9999, we need to divide the exponent (9999) by 4 and find the remainder.
9999 รท 4 = 2499 remainder 3
Since the remainder is 3, the last digit of 3^9999 will be the third element in the repeating pattern, which is 7.
Therefore, the last digit in 3^9999 is 7.