# 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 \( \sqrt[m]{M}?\)