what is the unit digit of 7^49?
I solved it and got the answer 07, but I'm not sure if it's correct.
To find the unit digit of a number raised to a power, we need to look for a pattern.
Let's start by listing the unit digits of powers of 7:
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = 2401
7^5 = 16807
...
From the pattern, we can observe that the unit digit of 7^1 is 7, the unit digit of 7^2 is 9, the unit digit of 7^3 is 3, and so on. Notice that the unit digits repeat in a cycle: 7, 9, 3, 1.
Since the cycle length is 4, we can find the unit digit of any power of 7 by taking the remainder of the exponent when divided by 4.
In this case, 49 divided by 4 gives a remainder of 1. Therefore, the unit digit of 7^49 is the same as the unit digit of 7^1, which is 7.
Therefore, your answer of 07 is correct.