Final answer:
The units digit of 3^2020 is found by examining the repeating pattern of the units digits when 3 is raised to successive powers. The pattern repeats every 4 powers, and the units digit coincides with the final digit in the pattern after full cycles, which is 1.
Step-by-step explanation:
The student is asking what the units digit (also known as the ones digit) is of the number 32020. To determine the unit digit of a large exponent, we focus on the pattern of units digits that the base number produces when it is raised to increasing powers. When we raise 3 to any power, the pattern of the units digit repeats every 4 powers, as follows:
- 31 has a unit digit of 3,
- 32 has a unit digit of 9,
- 33 has a unit digit of 7,
- 34 has a unit digit of 1,
and then the pattern repeats. To find the units digit of 32020, we divide the exponent 2020 by 4 to find the remainder. The remainder after dividing 2020 by 4 is 0, which means that we complete a full cycle and the units digit coincides with the final digit in the pattern: 1.
Therefore, the units digit of 32020 is 1.