Question

For any natural number n, \(6^n\) ends with the digit :

• A. 0
• B. 6
• C. 3
• D. 2

Hint:

The digits 0, 1, 5, and 6 always maintain their own value at the units place for any power \( n>0 \). (e.g., \( 5^n \) always ends in 5).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The "last digit" or "units digit" of a power follows a cyclical pattern. For the base 6, we can observe the powers to find the cycle.
Step 2: Key Formula or Approach:
Calculate the first few powers of 6 to identify the pattern.
Step 3: Detailed Explanation:
1. \( 6^1 = 6 \) 2. \( 6^2 = 36 \) 3. \( 6^3 = 216 \) 4. \( 6^4 = 1296 \) Observation: Regardless of the power \( n \), the product of any number ending in 6 multiplied by 6 will always result in a number ending in 6 (\( 6 \times 6 = 36 \)).
Step 4: Final Answer:
For any natural number \( n \), \( 6^n \) ends with the digit 6.