Simplify and express each of the following in exponential form:
`(2^(3)xx2)^2`

Answer

To simplify the expression \((2^{3} \times 2)^2\) and express it in exponential form, we can follow these steps:

### Step-by-Step Solution:

1. **Rewrite the Expression**:
Start with the given expression:
\[ (2^{3} \times 2)^2 \]

2. **Use the Property of Exponents**:
We know that \(2\) can be expressed as \(2^{1}\). Therefore, we can rewrite the expression as:
\[ (2^{3} \times 2^{1})^2 \]

3. **Apply the Product of Powers Property**:
According to the property of exponents, \(a^{m} \times a^{n} = a^{m+n}\). Thus, we can combine the exponents:
\[ (2^{3 + 1})^2 = (2^{4})^2 \]

4. **Use the Power of a Power Property**:
Now, apply the property that states \((a^{m})^{n} = a^{m \times n}\):
\[ 2^{4 \times 2} = 2^{8} \]

5. **Final Result**:
Therefore, the simplified expression in exponential form is:
\[ 2^{8} \]