Find the units digit in 23^7777 by looking for mod 10.
To find the units digit in a number raised to a power, we can use the concept of modular arithmetic. In this case, we can look for the units digit of the number 23 raised to the power of 7777 using modulo 10.
Modulo 10 means finding the remainder when a number is divided by 10. The units digit of a number is essentially the remainder when it is divided by 10.
Let's start by finding the pattern for the units digit of powers of 23:
23^1 = 23 (units digit: 3)
23^2 = 529 (units digit: 9)
23^3 = 12167 (units digit: 7)
23^4 = 279841 (units digit: 1)
23^5 = 6436343 (units digit: 3)
We can see that the units digit repeats in a pattern of 3, 9, 7, 1. This means that for any power of 23, we only need to consider the remainder when the power is divided by 4 (as the pattern repeats after every 4 powers).
Now let's calculate the remainder when 7777 is divided by 4:
7777 ÷ 4 = 1944 remainder 1
Since the remainder is 1, we need to find the units digit of 23^1, which is 3.
Therefore, the units digit in 23^7777 is 3.