What would be the digit in the 10th place of `7^n` where 'n' is a natural number greater than 1 ?

Options

A. 0,1,4,6
B. 1,2,3,8
C. 5,6,9
D. 0,4

Answer

To find the digit in the 10th place of \(7^n\) where \(n\) is a natural number greater than 1, we can calculate the values of \(7^n\) for different values of \(n\) and observe the digit in the 10th place.

### Step-by-Step Solution:

1. **Calculate \(7^2\)**:
\[ 7^2 = 49 \]
The digit in the 10th place is **4**.

2. **Calculate \(7^3\)**:
\[ 7^3 = 343 \]
The digit in the 10th place is **4**.

3. **Calculate \(7^4\)**:
\[ 7^4 = 2401 \]
The digit in the 10th place is **0**.

4. **Calculate \(7^5\)**:
\[ 7^5 = 16807 \]
The digit in the 10th place is **0**.

5. **Calculate \(7^6\)**:
\[ 7^6 = 117649 \]
The digit in the 10th place is **4**.

6. **Calculate \(7^7\)**:
\[ 7^7 = 823543 \]
The digit in the 10th place is **4**.

7. **Calculate \(7^8\)**:
\[ 7^8 = 5764801 \]
The digit in the 10th place is **0**.

8. **Calculate \(7^9\)**:
\[ 7^9 = 40353607 \]
The digit in the 10th place is **0**.

9. **Calculate \(7^{10}\)**:
\[ 7^{10} = 282475249 \]
The digit in the 10th place is **4**.

### Conclusion:
From the calculations, we observe that the digit in the 10th place alternates between **4** and **0** for different values of \(n\). Specifically:
- For \(n = 2, 3, 6, 7, 10\), the digit is **4**.
- For \(n = 4, 5, 8, 9\), the digit is **0**.

Thus, the digit in the 10th place of \(7^n\) where \(n\) is a natural number greater than 1 can be either **0** or **4**.

### Final Answer:
The digit in the 10th place of \(7^n\) for \(n > 1\) is either **0** or **4**.