Question

What is the reason for 7 to the power of 7 ending with 7 as it's units place?

Answer 1

7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
7^7=823543
that means after avery 5th digit te same nos end as units place as 7,9,3,1
as a result we dont  get its units palce as 7
hope it helps you frn

Answer 2

There is a unique cycle that is repeated when we raise a number to an exponent. Here is an example of 7,
7^0=1
7^1=7
7^2=49
7^3=343
7^4=2401
7^5=16807
7^6=117649
7^7=823543

See, the cycle is 1-7-9-3-1-7-9-3....

And the question is What is the reason for 7 to the power of 7 ending with 7 as it's units place?But here we see that 7^7 has no 7 at its units place but 7^5 has. Instead 7^7 has 3 at its units place. 
Hence, the question is actually wrong. But if asked we can write this as the answer.

Hope it helps...!