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 convert the expression `8 x 8 x 8 x 8` into exponential form with base 2, follow these steps:

### Step-by-Step Solution:

1. **Identify the base and count the number of times it appears**:
- The number 8 is multiplied by itself 4 times:
\[ 8 \times 8 \times 8 \times 8 = 8^4 \]

2. **Express 8 in terms of base 2**:
- We know that \(8\) can be expressed as \(2^3\) because:
\[ 2 \times 2 \times 2 = 8 \quad \text{(or } 2^3 = 8\text{)} \]

3. **Substitute \(8\) with \(2^3\) in the exponential expression**:
- Now we can rewrite \(8^4\) as:
\[ (2^3)^4 \]

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

5. **Calculate the exponent**:
- Now calculate \(3 \cdot 4\):
\[ 3 \cdot 4 = 12 \]
- Therefore, we have:
\[ 2^{12} \]

### Final Answer:
The exponential form of \(8 \times 8 \times 8 \times 8\) taking base 2 is:
\[ 2^{12} \]