In the following, which is the greatest number?

Options

A. `(3xx3xx3)^2`
B. `(9)^2`
C. `(3+3+3)^2`
D. `[(3+3)^2]^(2)`

Answer

To determine which is the greatest number among the given expressions, let's evaluate each one step by step.

### Step 1: Calculate \(3 \times 3 \times 3\) and then square it.
- First, we calculate \(3 \times 3 \times 3\):
\[ 3 \times 3 = 9 \]
\[ 9 \times 3 = 27 \]
- Now, we square \(27\):
\[ 27^2 = 729 \]

### Step 2: Calculate \(9^2\).
- We calculate the square of \(9\):
\[ 9^2 = 81 \]

### Step 3: Calculate \(3 \times 3 \times 3\) again, which we already know is \(27\), and then square it.
- We already found that \(3 \times 3 \times 3 = 27\), so we square it again:
\[ 27^2 = 729 \]

### Step 4: Calculate \(3 \times 3\) and then square it.
- First, we calculate \(3 \times 3\):
\[ 3 \times 3 = 9 \]
- Now, we square \(9\):
\[ 9^2 = 81 \]

### Step 5: Calculate \(6^2\).
- We calculate the square of \(6\):
\[ 6^2 = 36 \]

### Step 6: Calculate \(36^2\).
- Now, we square \(36\):
\[ 36^2 = 1296 \]

### Summary of Results:
- From Step 1: \(27^2 = 729\)
- From Step 2: \(9^2 = 81\)
- From Step 3: \(27^2 = 729\)
- From Step 4: \(9^2 = 81\)
- From Step 6: \(36^2 = 1296\)

### Conclusion:
The greatest number among the calculated values is \(1296\).

### Final Answer:
Thus, the greatest number is \(36^2\), which equals \(1296\).

---