How do you solve powers of powers in advanced algebra

Ex: 2^2^2

Basically, the base is multiplied by the first power however large the number. Then the new base is multiplied by the second power to get an even larger number.
Say you have a question that asks for the power of the power of 2. Or 2^2^2.

You would do the equation 2^2 first, and end up with 4. But since you have another power, you would have the answer as 4^2. Which would then equal 16. But another equation that is similar is: 2^2^2 = 2^4
The two equations would still get the same answer, but would look entirely different.