what is the digit in the unit's plase of

1. (143) to power 86?
2. (249)to power 98?
3. (125)to power 34?

since 86 = 4*21+2 i.e. of the type 4n+2.
$3^1=3; 3^2=9; 3^3=27; 3^4=81$
if the power is of the type 4n+2, unit digit is 9.

2.   since 98 = 24*4+2
$9^1=9; 9^2=81;$
the digit at the unit place of (249)^98 is 1.
if the power is even, digit at the unit place of 249^m is 1.
if the power is odd , digit at the unit place of 249^m is 9

3.
if a number ends with 5, the unit digit of any power of that number is 5.
(125)^n ends with 5 [where n is an integer.

hope this helps you