`11^(2) + 11^(4) div 11^(3)` of `11 -11 = ?`

Options

A. 111
B. 121
C. 131
D. 101

Answer

To solve the expression \( 11^2 + \frac{11^4}{11^3} - 11 \), we will follow the order of operations, often referred to as BODMAS/BIDMAS (Brackets, Orders (i.e., powers and roots, etc.), Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Identify the expression**:
\[ 11^2 + \frac{11^4}{11^3} - 11 \]

2. **Simplify the division**:
\[ \frac{11^4}{11^3} = 11^{4-3} = 11^1 = 11 \]
So, we can rewrite the expression as:
\[ 11^2 + 11 - 11 \]

3. **Now simplify the expression**:
\[ 11^2 + 11 - 11 = 11^2 + (11 - 11) \]
Since \( 11 - 11 = 0 \), we have:
\[ 11^2 + 0 = 11^2 \]

4. **Calculate \( 11^2 \)**:
\[ 11^2 = 121 \]

5. **Final result**:
The final answer is:
\[ 121 \]

### Summary of Steps:
1. Simplify the division \( \frac{11^4}{11^3} \) to get \( 11 \).
2. Substitute back into the expression.
3. Simplify \( 11^2 + 11 - 11 \) to \( 11^2 \).
4. Calculate \( 11^2 \) to find the final answer.