First, in terms of tetration (formula_10) alone::formula_11where the number of 3s in the expression on the right is:formula_12Now each tetration (formula_13) operation reduces to a "tower" of exponentiations (formula_14) according to the definition:formula_15Thus,:formula_16becomes, solely in terms of repeated "exponentiation towers",:formula_17and where the number of 3s in each tower, starting from the leftmost tower, is specified by the value of the next tower to the right.
First, in terms of tetration (formula_16) alone::formula_17where the number of 3s in the expression on the right is:formula_18Now each tetration (formula_19) operation reduces to a "tower" of exponentiations (formula_20) according to the definition:formula_21Thus,:formula_22becomes, solely in terms of repeated "exponentiation towers",:formula_23and where the number of 3s in each tower, starting from the leftmost tower, is specified by the value of the next tower to the right.