Finding Units Digit of x^n

The units digit of a number raised to a power follows a repeating cycle. To find the units digit of $x^n$, you can use this pattern.

Procedure:

1. Identify the cycle of the units digits for powers of the base's units digit. For example, for powers of 3, the units digits cycle is 3, 9, 7, 1 (a cycle of length 4).
2. Find the remainder when the exponent $n$ is divided by the length of the cycle. Let the remainder be $r$. (If the remainder is 0, use the last digit in the cycle).
3. The units digit of $x^n$ is the same as the $r$-th digit in the cycle.

For $3^{47}$: The cycle length is 4. $47 \div 4$ has a remainder of 3. The 3rd digit in the cycle (3, 9, 7, 1) is 7. So, the units digit of $3^{47}$ is 7.