2^2^2^2

To evaluate \(2^{2^{2^2}}\), we can break it down step-by-step:

1. Start with the innermost exponent: \[ 2^2 = 4 \]

2. Next, use the result from step 1 as the exponent for the next power of 2: \[ 2^{(2^2)} = 2^4 = 16 \]

3. Finally, use the result from step 2 as the exponent for the outermost power of 2: \[ 2^{(2^{2^2})} = 2^{16} \]

4. Now calculate \(2^{16}\): \[ 2^{16} = 65536 \]

So, \(2^{2^{2^2}} = 65536\).