Which of the following is largest?

Options

A. `(2+2+2)^(2)`
B. `[(2+2+2)^(2)]^(2)`
C. `(2xx2xx2)^(2)`
D. `2+2^(2)+(2^(2))^(2)`

Explanation

To determine which of the given expressions is the largest, we will evaluate each option step by step.

### Step 1: Evaluate the first option
The first option is \( (2 + 2 + 2)^2 \).

1. Calculate \( 2 + 2 + 2 \):
\[ 2 + 2 + 2 = 6 \]
2. Now, square the result:
\[ 6^2 = 36 \]

### Step 2: Evaluate the second option
The second option is \( (2 + 2 + 2)^2 \) again, but we will interpret it as \( (2 + 2 + 2)^2 \) which is the same as the first option.

1. Calculate \( 2 + 2 + 2 \):
\[ 2 + 2 + 2 = 6 \]
2. Now, square the result:
\[ 6^2 = 36 \]

### Step 3: Evaluate the third option
The third option is \( (2 \times 2 \times 2)^2 \).

1. Calculate \( 2 \times 2 \):
\[ 2 \times 2 = 4 \]
2. Now, multiply by 2:
\[ 4 \times 2 = 8 \]
3. Now, square the result:
\[ 8^2 = 64 \]

### Step 4: Evaluate the fourth option
The fourth option is \( (2 + 2^2 + 2^2)^2 \).

1. Calculate \( 2^2 \):
\[ 2^2 = 4 \]
2. Now, add \( 2 + 2^2 + 2^2 \):
\[ 2 + 4 + 4 = 10 \]
3. Now, square the result:
\[ 10^2 = 100 \]

### Summary of Results
- First option: \( 36 \)
- Second option: \( 36 \)
- Third option: \( 64 \)
- Fourth option: \( 100 \)

### Conclusion
The largest value is from the fourth option, which is \( 100 \).