Select the correct option.

Options

A. Exponent - `3^(5)`, Base -3, Value - 87
B. Exponent - `2^(4)`, Base -5, Value - 32
C. Exponent - `4^(2)`, Base -4, Value - 16
D. Exponent - `5^(2)`, Base -5, Value - 125

Answer

To solve the question of selecting the correct option based on the given exponents and their values, we will analyze each option step by step.

### Step-by-Step Solution:

1. **Understanding Exponents**:
- An exponent is a way to express repeated multiplication of a number. The expression \( x^n \) means that the base \( x \) is multiplied by itself \( n \) times.

2. **Analyzing Option 1**:
- **Expression**: \( 3^5 \)
- **Base**: 3
- **Value Calculation**:
\[ 3^5 = 3 \times 3 \times 3 \times 3 \times 3 \]
- Calculate step by step:
- \( 3 \times 3 = 9 \)
- \( 9 \times 3 = 27 \)
- \( 27 \times 3 = 81 \)
- \( 81 \times 3 = 243 \)
- **Result**: The value is 243, not 87.
- **Conclusion**: Option 1 is incorrect.

3. **Analyzing Option 2**:
- **Expression**: \( 2^4 \)
- **Base**: 2
- **Value Calculation**:
\[ 2^4 = 2 \times 2 \times 2 \times 2 \]
- Calculate step by step:
- \( 2 \times 2 = 4 \)
- \( 4 \times 2 = 8 \)
- \( 8 \times 2 = 16 \)
- **Result**: The value is 16, not 5.
- **Conclusion**: Option 2 is incorrect.

4. **Analyzing Option 3**:
- **Expression**: \( 4^2 \)
- **Base**: 4
- **Value Calculation**:
\[ 4^2 = 4 \times 4 \]
- Calculate:
- \( 4 \times 4 = 16 \)
- **Result**: The value is 16.
- **Conclusion**: Option 3 is correct.

5. **Analyzing Option 4**:
- **Expression**: \( 5^2 \)
- **Base**: 5
- **Value Calculation**:
\[ 5^2 = 5 \times 5 \]
- Calculate:
- \( 5 \times 5 = 25 \)
- **Result**: The value is 25, not 5.
- **Conclusion**: Option 4 is incorrect.

### Final Answer:
The correct option is **Option 3**.