What is the units digit of 13^86?

lheiannie07 wrote:What is the units digit of 13^86?

A. 1
B. 3
C. 5
D. 7
E. 9

Since we only care about units digits, we can rewrite the expression as:

3^86

Let’s start by evaluating the pattern of the units digits of 3^n for positive integer values of n. That is, let’s look at the pattern of the units digits of powers of 3. When writing out the pattern, notice that we are ONLY concerned with the units digit of 3 raised to each power.

3^1 = 3

3^2 = 9

3^3 = 7

3^4 = 1

3^5 = 3

The pattern of the units digit of powers of 3 repeats every 4 exponents. The pattern is 3–9–7–1. In this pattern, all positive exponents that are multiples of 4 will produce a 1 as the units digit. Thus:

3^84 has a units digit of 1, 3^85 has a units digit of 3, and 3^86 has a units digit of 9.

Answer: E