So i have 7^900413 and want to know what the second last number is if we had done the calculation.
Start this way:
7^0 = 001
7^1 = 007
7^2 = 049
7^3 = x43
7^4 = x01
7^5 = x07
7^6 = x49
7^7 = x43
7^8 = x01
7^9 = x07
Next to the last digit is either 0 or 4.
Notice that the digits occur in pairs.
The zero first occurs when the exponent is:
0,4,8,12,16,20,etc...
or in steps of 4.
900413 divided by 4 is some number with remainder of 1
Thus the last two digits of 7^900412 = 01
You need to do one more calculation.
.