2¹⁴¹! Unit digeet

Question

2¹⁴¹! Unit digeet

ScanSolve AI Tutor · Accepted Answer

Step 1: To find the unit digit of 2¹⁴¹, we need to observe the pattern of the unit digits of powers of 2. The powers of 2 are: 2¹ = 2; 2² = 4; 2³ = 8; 2⁴ = 16 (unit digit is 6); 2⁵ = 32 (unit digit is 2); 2⁶ = 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 2¹⁴¹, 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 2¹⁴¹ will be the same as the first unit digit in the cycle, which is the unit digit of 2¹. Step 6: The unit digit of 2¹ is 2. Therefore, the unit digit of 2¹⁴¹ is 2. 2

2¹⁴¹! Unit digeet

Answer

Step-by-step solution

To find the unit digit of $2^{141}$ , we need to observe the pattern of the unit digits of powers of 2.

The pattern of the unit digits of powers of 2 is 2, 4, 8, 6, and this cycle repeats every 4 powers.

To find the unit digit of $2^{141}$ , we need to find the remainder when the exponent 141 is divided by 4.

Performing the division

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 $2^1$ .

The unit digit of $2^1$ is 2.

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2¹⁴¹! Unit digeet

Answer

Step-by-step solution

To find the unit digit of 21412^{141}2141, we need to observe the pattern of the unit digits of powers of 2.

The pattern of the unit digits of powers of 2 is 2, 4, 8, 6, and this cycle repeats every 4 powers.

To find the unit digit of 21412^{141}2141, we need to find the remainder when the exponent 141 is divided by 4.

Performing the division

Since the remainder is 1, the unit digit of 21412^{141}2141 will be the same as the first unit digit in the cycle, which is the unit digit of 212^121.

The unit digit of 212^121 is 2.

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More Mathematics Questions

To find the unit digit of $2^{141}$ , we need to observe the pattern of the unit digits of powers of 2.

To find the unit digit of $2^{141}$ , we need to find the remainder when the exponent 141 is divided by 4.

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 $2^1$ .

The unit digit of $2^1$ is 2.