Question

find unit digit of (17 raised to the power 27)

Answer 1

· Identify the units digit in the base 'x' and call it say 'l'. {For example, If x = 24, then the units digit in 24 is 4. Hence l = 4.}
· Divide the exponent 'y' by 4. If the exponent y is exactly divisible by 4. i.e, y leaves a remainder 0 when divided by 4. hope this helpful you

Answer 2

7×7 = 49
9×7 = 63
3×7 = 21
1×7 = 7

27÷4 = 6 + rem(3)

hence the unit place will be 1. when you calculate the powers of 17, the units place will depend only on the multiplication of the unit place, ie , 7, in our case. So, when we calculate powers of 17, the pattern as shown above repeats every fourth time.
so, you just need to find out the remainder of 27/4 which is 3. so you will get the unit place digit we got in the 3rd multiplication.