The largest number among the following is

Options

A. `3^(2^(2^(2)))`
B. `{ (3^2)^2}^2`
C. `3^(2) xx 3^(2) xx 3^(2)`
D. `3222`

Answer

To find the largest number among the given options, we will evaluate each expression step by step.

### Step 1: Evaluate Option A: \(3^{2^{2^2}}\)

1. Start with the innermost exponent:
\[ 2^2 = 4 \]
2. Now substitute back into the expression:
\[ 3^{2^4} \]
3. Evaluate \(2^4\):
\[ 2^4 = 16 \]
4. Therefore, we have:
\[ 3^{16} \]

### Step 2: Evaluate Option B: \( (3^2)^4 \)

1. Start by evaluating \(3^2\):
\[ 3^2 = 9 \]
2. Now raise this to the power of 4:
\[ 9^4 \]
3. Rewrite \(9\) as \(3^2\):
\[ (3^2)^4 = 3^{2 \times 4} = 3^8 \]

### Step 3: Evaluate Option C: \(3^2 \times 3^2 \times 3^2\)

1. We can combine the exponents since the bases are the same:
\[ 3^2 \times 3^2 \times 3^2 = 3^{2 + 2 + 2} = 3^6 \]

### Step 4: Evaluate Option D: \(3222\)

This is a constant number and does not need further evaluation.

### Step 5: Compare the results

Now we have:
- Option A: \(3^{16}\)
- Option B: \(3^8\)
- Option C: \(3^6\)
- Option D: \(3222\)

### Step 6: Determine the largest number

1. Compare \(3^{16}\), \(3^8\), \(3^6\), and \(3222\):
- \(3^{16}\) is significantly larger than \(3^8\) and \(3^6\).
- \(3^8 = 6561\) which is greater than \(3222\).
- \(3^6 = 729\) which is less than \(3222\).

Thus, the largest number is:
\[ \text{Option A: } 3^{16} \]

### Final Answer:
The largest number among the given options is \(3^{2^{2^2}}\) or \(3^{16}\).

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