01 / GROUP THE BASE
10 DIGITS
nine to the tenth
(3^2)^10 = 9^10
3,486,784,401
EXHIBIT 08 / ARITHMETIC
TOWER
Three squared to the power of ten can be nine to the tenth, three to the two-to-the-tenth, or six to the tenth. Change the numbers. All three readings stay up.
3^2^10
three squared to the power of ten
02 / RIGHT-ASSOCIATIVE
489 DIGITS
three to the two-to-the-tenth
3^(2^10) = 3^1024
373,391,848,741,020,043,532,959,754,184,866,588,225,409,776,783,734,007,750,636,931,722,079,040,617,265,251,229,993,688,938,803,977,220,468,765,065,431,475,158,108,727,054,592,160,858,581,351,336,982,809,187,314,191,748,594,262,580,938,807,019,951,956,404,285,571,818,041,046,681,288,797,402,925,517,668,012,340,617,298,396,574,731,619,152,386,723,046,235,125,934,896,058,590,588,284,654,793,540,505,936,202,376,547,807,442,730,582,144,527,058,988,756,251,452,817,793,413,352,141,920,744,623,027,518,729,185,432,862,375,737,063,985,485,319,476,416,926,263,819,972,887,006,907,013,899,256,524,297,198,527,698,749,274,196,276,811,060,702,333,710,356,481
03 / HEARD AS TIMES
8 DIGITS
six to the tenth
(3×2)^10 = 6^10
60,466,176
Written math is right-associative, so the tower is the convention. Grouping the base is the other legal reading. The product is what happens when “squared” is heard as “times two.” None of them are hidden.