This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: To find the unit digit of 2^141, we need to observe the pattern of the unit digits of powers of 2. The powers of 2 are: 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 (unit digit is 6) 2^5 = 32 (unit digit is 2) 2^6 = 64 (unit digit is 4) Step 2: The pattern of the unit digits of powers of 2 is 2, 4, 8, 6, and this cycle repeats every 4 powers. Step 3: To find the unit digit of 2^141, we need to find the remainder when the exponent 141 is divided by 4. 141 ÷ 4 Step 4: Performing the division: 141 = 4 × 35 + 1 The remainder is 1. Step 5: Since the remainder is 1, the unit digit of 2^141 will be the same as the first unit digit in the cycle, which is the unit digit of 2^1. Step 6: The unit digit of 2^1 is 2. Therefore, the unit digit of 2^141 is 2. 2 अगला प्रश्न भेजें 📸