Find the unit digit in the given product `(4211)^(102) xx (361)^(52)`

A. 3

B. 1

C. 4.

D. 7

Options

A. A
B. D
C. B
D. C

Answer

To find the unit digit of the product \( (4211)^{102} \times (361)^{52} \), we can follow these steps:

### Step 1: Identify the unit digits
First, we need to identify the unit digits of the numbers involved in the product.

- The unit digit of \( 4211 \) is \( 1 \).
- The unit digit of \( 361 \) is \( 1 \).

### Step 2: Calculate the unit digits of the powers
Next, we will calculate the unit digit of each term raised to their respective powers.

- The unit digit of \( (4211)^{102} \):
Since the unit digit of \( 4211 \) is \( 1 \), any power of \( 1 \) will also have a unit digit of \( 1 \).
\[ \text{Unit digit of } (4211)^{102} = 1 \]

- The unit digit of \( (361)^{52} \):
Similarly, since the unit digit of \( 361 \) is \( 1 \), any power of \( 1 \) will also have a unit digit of \( 1 \).
\[ \text{Unit digit of } (361)^{52} = 1 \]

### Step 3: Multiply the unit digits
Now we can find the unit digit of the entire product:
\[ \text{Unit digit of } (4211)^{102} \times (361)^{52} = 1 \times 1 = 1 \]

### Conclusion
The unit digit of the product \( (4211)^{102} \times (361)^{52} \) is \( 1 \).

### Final Answer
Thus, the answer is \( \text{B. } 1 \).

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