`{:("Column A"," ","Column B"),((2^(20) - 2^(19))/(2^11),,2^(8)):}`

Options

A. If column A is larger
B. If column B is larger
C. If the columns are equal
D. If there is not enough information to decide

Answer

To solve the problem, we need to simplify the expression in Column A and compare it with the value in Column B.

### Step-by-Step Solution:

1. **Identify Column A**:
\[ \text{Column A} = \frac{2^{20} - 2^{19}}{2^{11}} \]

2. **Factor out the common term in the numerator**:
- In the numerator \(2^{20} - 2^{19}\), we can factor out \(2^{19}\):
\[ 2^{20} - 2^{19} = 2^{19}(2^1 - 1) = 2^{19}(2 - 1) = 2^{19}(1) \]
- Therefore, Column A becomes:
\[ \text{Column A} = \frac{2^{19} \cdot 1}{2^{11}} \]

3. **Simplify the fraction**:
- Using the law of exponents, \(\frac{A^M}{A^N} = A^{M-N}\):
\[ \text{Column A} = 2^{19 - 11} = 2^{8} \]

4. **Identify Column B**:
\[ \text{Column B} = 2^{8} \]

5. **Compare Column A and Column B**:
- We find that both Column A and Column B are equal:
\[ \text{Column A} = 2^{8} \quad \text{and} \quad \text{Column B} = 2^{8} \]

### Conclusion:
Since both columns are equal, the answer is that Column A is equal to Column B.