Write exponential form for `8 xx 8 xx 8 xx 8` taking base as `2.`

Options

A. `2^12`
B. `2^6`
C. `2^8`
D. `2^10`

Explanation

To write the exponential form of \( 8 \times 8 \times 8 \times 8 \) with base \( 2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the number of times 8 is multiplied**:
- We have \( 8 \) multiplied by itself \( 4 \) times: \( 8 \times 8 \times 8 \times 8 \).

2. **Express 8 in terms of base 2**:
- We know that \( 8 = 2^3 \). This means we can rewrite each \( 8 \) as \( 2^3 \).

3. **Rewrite the expression using base 2**:
- Substitute \( 8 \) with \( 2^3 \):
\[ 8 \times 8 \times 8 \times 8 = (2^3) \times (2^3) \times (2^3) \times (2^3) \]

4. **Use the property of exponents**:
- When multiplying like bases, we add the exponents. Since we have \( 4 \) terms of \( 2^3 \), we can express this as:
\[ (2^3)^4 \]

5. **Apply the power of a power property**:
- According to the exponent rule \( (a^m)^n = a^{m \cdot n} \), we can multiply the exponents:
\[ (2^3)^4 = 2^{3 \times 4} = 2^{12} \]

6. **Final result**:
- Therefore, the exponential form of \( 8 \times 8 \times 8 \times 8 \) with base \( 2 \) is:
\[ 2^{12} \]