Question

5.Find the unit digit of (3456825)^128 X (4567)^41​

Answer 1

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

Answer 2

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.