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.