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 expressions, we will evaluate each expression step by step.

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

1. Start with the innermost exponent: \(2^2 = 4\).
2. Now substitute this back: \(3^{2^4}\).
3. Next, calculate \(2^4 = 16\).
4. Therefore, we have \(3^{16}\).

### Step 2: Evaluate \(3^{2 \times 2 \times 2}\)

1. Here, calculate the multiplication in the exponent: \(2 \times 2 \times 2 = 8\).
2. So, this expression simplifies to \(3^8\).

### Step 3: Evaluate \(3^{2 + 2 + 2}\)

1. Add the exponents: \(2 + 2 + 2 = 6\).
2. Thus, this expression simplifies to \(3^6\).

### Step 4: Compare the values

Now we have three expressions to compare:
- \(3^{16}\)
- \(3^8\)
- \(3^6\)

Since all the bases are the same (3), we can compare the exponents directly:
- \(16 > 8 > 6\)

### Conclusion

The largest number among the given expressions is \(3^{16}\), which corresponds to the expression \(3^{2^{2^{2}}}\).

### Final Answer
The largest number is \(3^{2^{2^{2}}}\).

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