# The answer is written everywhere

Algebra Level 3

$\Large 2^{2^{2^{2^2}}}$

If I were to insert a pair of parentheses into the number above, the resultant value might differ. For example, by adding the parentheses like

$\Large 2^{2^{2^{\left(2^2\right)}}},$

we would have the same result. But if I were to add the parentheses like

$\Large \left(2^2\right)^{2^{2^2}},$

the resultant number would not remain the same.

If we're only allowed to add exactly one pair of parentheses as shown above, find the minimum value (call it $$m$$) and the maximum value (call it $$M$$) of all the possible resultant numbers.

Then what is $$\sqrt[m]{M}?$$

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