Is there a notation for exponentiation analog to capital-sigma notation Σ for addition and capital pi Π notation for multiplications?

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There are the following common notations:

  • Sums: $$\sum_{i=2}^4 i = 2 + 3 + 4 = 9$$
  • Products: $$\prod_{i=2}^4 i = 2\times 3\times 4 = 24$$

Is there a (theoretical) one for:

  • Exponentiation (conventional/top down) $$\ X_{i=2}^4 i = {2 ^ {3^4}} = 2^{81} =2\,417\,851\,639\,229\,258\,349\,412\,352$$

There is probably no need for of having a special notation for non-conventional Exponents (bottom up) like ${{2 ^ 3}^4} = 2 ^ {3\times4} = 4096$ in the first place. Since this is equivalent to $$n^{\prod_{i=n+1}^4 i} ;n=2$$

Or does this type of notation anyway only make sense for associative and commutative operations; or is this just too exotic?