5.Find the unit digit of (3456825)^128 X (4567)^41
Answers
Step-by-step explanation:
unit digit of (3456825)^128
always = 5
unit digit of (4567)^41
repeat after power 4 so 41/4 = 10
remains 1
so 7 power 1 = 7
unit digit of (3456825)^128 X (4567)^41
5×7 = 35
so unit digit is 5
Step-by-step explanation:
unit digit of 3456825^128 is same as unit digit of 5^128
so now, we know
5^1=5
5^2=25
5^3=125
5^5=625 and so on...
here every digit that is with power 5 we get its unit digit as 5.
and again,
unit digit of 4567^41 is same as unit digit of 7^41
now we know,
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807 and so on....
the cycle repeats
here when we multiply with the 1 we got unit digit as 7.
so here finally the unit digit is 7
Now let us find the unit digit of the (3456825)^128 X (4567)^41
i.e last unit digit of 4567^41 and 3456825^128 we get as- 7*5 =35
and finally the ans is 5.