what is the lsst digit of 2³³?​

Answer:Here's how to find the last digit of 2³³: Understanding Cyclical Patterns The last digits of powers of 2 follow a cyclical pattern: - 2¹ = 2- 2² = 4- 2³ = 8- 2⁴ = 6- 2⁵ = 2 (The pattern repeats) Notice that the last digits cycle through 2, 4, 8, and 6. Finding the Last Digit 1. Divide the exponent by 4: 33 / 4 = 8 remainder 12. The remainder tells you where you are in the cycle: A remainder of 1 means the last digit is the same as 2¹. Therefore, the last digit of 2³³ is 2.

Answered by coquetteyhin | 2024-09-06

Step-by-step explanation:To find the last digit of \(2^{33}\), we can look at the pattern in the last digits of the powers of 2:- \(2^1 = 2\) (last digit 2)- \(2^2 = 4\) (last digit 4)- \(2^3 = 8\) (last digit 8)- \(2^4 = 16\) (last digit 6)- \(2^5 = 32\) (last digit 2)- \(2^6 = 64\) (last digit 4)- \(2^7 = 128\) (last digit 8)- \(2^8 = 256\) (last digit 6)The last digits repeat in a cycle of 4: 2, 4, 8, 6. To find the last digit of \(2^{33}\), we determine the position of 33 in this cycle. Calculate \(33 \mod 4\):\[ 33 \div 4 = 8 \text{ remainder } 1 \]So, \(33 \mod 4 = 1\), which means the last digit of \(2^{33}\) corresponds to the last digit of \(2^1\), which is 2. Therefore, the last digit of \(2^{33}\) is 2.

Answered by yanskie0188 | 2024-09-06