Which of the following is equal to 1?

Options

A. `2^(@)+3^(@)+4^(@)`
B. `2^(@)xx3^(@)xx4^(@)`
C. `(3^(@)-2^(@))xx4^(@)`
D. `(3^(@)-2^(@))xx(3^(@)+2^(@))`

Answer

To determine which of the given options is equal to 1, we will evaluate each option step by step.

### Step-by-Step Solution:

1. **Evaluate Option 1:**
\[ 2^0 + 3^0 + 4^0 \]
- According to the exponent rule, any non-zero number raised to the power of 0 is equal to 1.
- Therefore:
\[ 2^0 = 1, \quad 3^0 = 1, \quad 4^0 = 1 \]
- Now, substitute these values into the expression:
\[ 1 + 1 + 1 = 3 \]
- **Conclusion:** Option 1 is not equal to 1.

2. **Evaluate Option 2:**
\[ 2^0 \times 3^0 \times 4^0 \]
- Again, using the same exponent rule:
\[ 2^0 = 1, \quad 3^0 = 1, \quad 4^0 = 1 \]
- Substitute these values:
\[ 1 \times 1 \times 1 = 1 \]
- **Conclusion:** Option 2 is equal to 1.

3. **Evaluate Option 3:**
\[ 3^0 - 2^0 \]
- Using the exponent rule:
\[ 3^0 = 1, \quad 2^0 = 1 \]
- Substitute these values:
\[ 1 - 1 = 0 \]
- **Conclusion:** Option 3 is not equal to 1.

4. **Evaluate Option 4:**
\[ 3^0 - 2^0 \times 3^0 + 2^0 \]
- Again, using the exponent rule:
\[ 3^0 = 1, \quad 2^0 = 1 \]
- Substitute these values:
\[ 1 - (1 \times 1) + 1 = 1 - 1 + 1 = 1 \]
- **Conclusion:** Option 4 is equal to 1.

### Summary of Results:
- Option 1: 3 (not equal to 1)
- Option 2: 1 (equal to 1)
- Option 3: 0 (not equal to 1)
- Option 4: 1 (equal to 1)

### Final Answer:
The options that are equal to 1 are **Option 2 and Option 4**.