Question

What is the ones digit in the number 2^2007? Hint: Start with smaller exponents to find a pattern.

Answer 1

By examining the pattern of ones digits in powers of 2, we find that the ones digit repeats every 4 cycles. The ones digit of 2^2007 is determined by the remainder when 2007 is divided by 4, which gives us the ones digit of 2^3, or 8.

Step-by-step explanation:

To find the ones digit in the number 2^2007, we can start by examining the pattern of the ones digits in the powers of 2 with smaller exponents:

• 2^1 = 2
• 2^2 = 4
• 2^3 = 8
• 2^4 = 16 (ones digit is 6)
• 2^5 = 32 (ones digit is 2, pattern starts over)

The pattern in the ones digit is 2, 4, 8, 6, and then it repeats every 4 cycles. To determine the ones digit of 2^2007, we can find the remainder when 2007 is divided by 4, which is 3. Therefore, the ones digit of 2^2007 is the same as the ones digit of 2^3, which is 8.