Let's start with anything using the number 10, from just powers of 10 all the way to the limit of tetrational array BEAF!
decker = 10^^10 = {10, 10, 2}
(???) deckerplex = 10^^10^^10 = 10^^^3
(???) deckerduplex = 10^^10^^10^^10 = 10^^^4
(???) deckertriplex = 10^^10^^10^^10^^10 = 10^^^5
(???) deckerquadriplex = 10^^10^^10^^10^^10^^10 = 10^^^6
(???) grand decker = 10^^^10 = 10^^^10 = {10, 10, 3}
(???) grand grand decker = 10^^^10^^^10 = 10^^^^3
(???) grand grand grand decker = 10^^^10^^^10^^^10 = 10^^^^4
(???) grand grand grand grand decker = 10^^^10^^^10^^^10^^^10 = 10^^^^5
(???) great decker = 10^^^^10 = {10, 10, 4}
(???) great great decker = 10^^^^10^^^^10 = 10^^^^^3
(???) great great great decker = 10^^^^10^^^^10^^^^10 = 10^^^^^4
(???) fifth decker = 10^^^^^10 = {10, 10, 5}
(???) fifth decker-plexed = 10^^^^^10^^^^^10 = 10^^^^^^3
(???) sixth decker = 10^^^^^^10 = {10, 10, 6}
(???) seventh decker = 10^^^^^^^10 = {10, 10, 7}
(???) eighth decker = 10^^^^^^^^10 = {10, 10, 8}
(???) ninth decker = 10^^^^^^^^^10 = {10, 10, 9}
(???) tenth decker = 10^^^^^^^^^^10 = {10, 10, 10}
(???) expandecal = {10, 10, 1, 2}
(???) multiexpandecal = {10, 10, 2, 2}
(???) powerexpandecal = {10, 10, 3, 2}
(???) tetraexpandecal = {10, 10, 4, 2}
(???) pentaexpandecal = {10, 10, 5, 2}
(???) hexaexpandecal = {10, 10, 6, 2}
grand tridecal / (???) tridecadyad = {10, 10, 10, 2}
(???) explodecal = {10, 10, 1, 3}
(???) multiexplodecal = {10, 10, 2, 3}
(???) powerexplodecal = {10, 10, 3, 3}
(???) tetraexplodecal = {10, 10, 4, 3}
(???) tridecatri = {10, 10, 10, 3}
(???) detonodecal = {10, 10, 1, 4}
(???) multidetonodecal = {10, 10, 2, 4}
(???) powerdetonodecal = {10, 10, 3, 4}
(???) tridecatet = {10, 10, 10, 4}
(???) pentonodecal = {10, 10, 1, 5}
(???) multipentonodecal = {10, 10, 2, 5}
(???) tridecapent = {10, 10, 10, 5}
(???) hexonodecal = {10, 10, 1, 6}
(???) tridecahex = {10, 10, 10, 6}
(???) tridecahept = {10, 10, 10, 7}
(???) tridecaoct = {10, 10, 10, 8}
(???) tridecaenn = {10, 10, 10, 9}
(???) tridecadeck = {10, 10, 10, 10}
general = {10, 10, 10, 10}
generalplex = {10, 10, 10, {10, 10, 10, 10}}
(???) monologia-general = {10, 10, 1, 1, 2}
(???) dialogia-general = {10, 10, 2, 1, 2}
(???) trialogia-general = {10, 10, 3, 1, 2}
(???) tetralogia-general = {10, 10, 4, 1, 2}
(???) tridecalo-general = {10, 10, 10, 1, 2}
(???) expandecalo-general = {10, 10, 1, 2, 2}
(???) multiexpandecalo-general = {10, 10, 2, 2, 2}
(???) tridecadyado-general = {10, 10, 10, 2, 2}
(???) explodeco-general = {10, 10, 1, 3, 2}
(???) tridecatrio-general = {10, 10, 10, 3, 2}
(???) tridecateto-general = {10, 10, 10, 4, 2}
(???) tridecapento-general = {10, 10, 10, 5, 2}
(???) grand general / (???) generadyad = {10, 10, 10, 10, 2}
(???) monologia-generadyad = {10, 10, 1, 1, 3}
(???) dialogia-generadyad = {10, 10, 2, 1, 3}
(???) tridecalo-generadyad = {10, 10, 10, 1, 3}
(???) expandecalo-generadyad = {10, 10, 1, 2, 3}
(???) tridecadyado-generadyad = {10, 10, 10, 2, 3}
(???) tridecatrio-generadyad = {10, 10, 10, 3, 3}
(???) generatri = {10, 10, 10, 10, 3}
(???) monologia-generatri = {10, 10, 1, 1, 4}
(???) tridecalo-generatri = {10, 10, 10, 1, 4}
(???) tridecadyado-generatri = {10, 10, 10, 2, 4}
(???) generatet = {10, 10, 10, 10, 4}
(???) tridecalo-generatet = {10, 10, 10, 1, 5}
(???) generapent = {10, 10, 10, 10, 5}
(???) generahex = {10, 10, 10, 10, 6}
(???) generahept = {10, 10, 10, 10, 7}
pentadecal = {10, 10, 10, 10, 10}
pentadecalplex = {10, 10, 10, 10, {10, 10, 10, 10, 10}}
(???) monologia-pentadecal = {10, 10, 1, 1, 1, 2}
(???) dialogia-pentadecal = {10, 10, 2, 1, 1, 2}
(???) tridecalo-pentadecal = {10, 10, 10, 1, 1, 2}
(???) tridecadyado-pentadecal = {10, 10, 10, 2, 1, 2}
(???) tetradecalo-pentadecal = {10, 10, 10, 10, 1, 2}
(???) tridecalo-tetradecalo-pentadecal = {10, 10, 10, 1, 2, 2}
(???) tetradecadyado-pentadecal = {10, 10, 10, 10, 2, 2}
(???) tetradecatrio-pentadecal = {10, 10, 10, 10, 3, 2}
(???) pentadecadyad = {10, 10, 10, 10, 10, 2}
(???) tridecalo-pentadecadyad = {10, 10, 10, 1, 1, 3}
(???) tetradecalo-pentadecadyad = {10, 10, 10, 10, 1, 3}
(???) tetradecadyado-pentadecadyad = {10, 10, 10, 10, 2, 3}
(???) pentadecatri = {10, 10, 10, 10, 10, 3}
(???) tetradecalo-pentadecatri = {10, 10, 10, 10, 1, 4}
(???) pentadecatet = {10, 10, 10, 10, 10, 4}
(???) pentadecapent = {10, 10, 10, 10, 10, 5}
(???) pentadecahex = {10, 10, 10, 10, 10, 6}
hexadecal = {10, 10, 10, 10, 10, 10}
grand hexadecal = {10, 10, 10, 10, 10, {10, 10, 10, 10, 10, 10}}
(???) monologia-hexadecal = {10, 10, 1, 1, 1, 1, 2}
(???) tridecalo-hexadecal = {10, 10, 10, 1, 1, 1, 2}
(???) tetradecalo-hexadecal = {10, 10, 10, 10, 1, 1, 2}
(???) tetradecadyado-hexadecal = {10, 10, 10, 10, 2, 1, 2}
(???) pentadecalo-hexadecal = {10, 10, 10, 10, 10, 1, 2}
(???) pentadecadyado-hexadecal = {10, 10, 10, 10, 10, 2, 2}
(???) hexadecadyad = {10, 10, 10, 10, 10, 10, 2}
(???) pentadecalo-hexadecadyad = {10, 10, 10, 10, 10, 1, 3}
(???) hexadecatri = {10, 10, 10, 10, 10, 10, 3}
(???) hexadecatet = {10, 10, 10, 10, 10, 10, 4}
(???) hexadecapent = {10, 10, 10, 10, 10, 10, 5}
heptadecal = {10, 10, 10, 10, 10, 10, 10}
(???) pentadecalo-heptadecal = {10, 10, 10, 10, 10, 1, 1, 2}
(???) hexadecalo-heptadecal = {10, 10, 10, 10, 10, 10, 1, 2}
(???) heptadecadyad = {10, 10, 10, 10, 10, 10, 10, 2}
(???) heptadecatri = {10, 10, 10, 10, 10, 10, 10, 3}
(???) heptadecatet = {10, 10, 10, 10, 10, 10, 10, 4}
octadecal = {10, 10, 10, 10, 10, 10, 10, 10}
(???) octadecadyad = {10, 10, 10, 10, 10, 10, 10, 10, 2}
(???) octadecatri = {10, 10, 10, 10, 10, 10, 10, 10, 3}
ennadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10}
(???) ennadecadyad = {10, 10, 10, 10, 10, 10, 10, 10, 10}
iteral / (???) decadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 10 (1) 2}
(???) endecadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 11 (1) 2}
(???) dodecadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 12 (1) 2}
(???) pentadecadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 15 (1) 2}
(???) icosadecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 20 (1) 2}
(???) triantadecal = {10, 30 (1) 2}
(???) penintadecal = {10, 50 (1) 2}
(???) hectadecal = {10, 100 (1) 2}
(???) chiliadecal = {10, 1000 (1) 2}
(???) myriadecal = {10, 10000 (1) 2}
(???) ultadecal = {10, 10000000000 (1) 2} = {10, {10, 10} (1) 2}
duperdecal = {10, {10, 10, 10, 10, 10, 10, 10, 10, 10, 10} (1) 2} = {10, {10, 10 (1) 2} (1) 2} = {10, 3, 2 (1) 2}
truperdecal = {10, {10, {10, 10 (1) 2} (1) 2} (1) 2} = {10, 4, 2 (1) 2}
quadruperdecal = {10, {10, {10, {10, 10 (1) 2} (1) 2} (1) 2} (1) 2} = {10, 5, 2 (1) 2}
(???) double decker = {10, 10, 2 (1) 2}
(???) tridecbol = {10, 10, 10 (1) 2}
(???) generadual = {10, 10, 10, 10 (1) 2}
(???) pentadecadual = {10, 10, 10, 10, 10 (1) 2}
(???) hexadecadual = {10, 10, 10, 10, 10, 10 (1) 2}
(???) ladecal = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (1) 2} = {10, 10 (1) 3}
(???) tridectrol = {10, 10, 10 (1) 3}
emperal = {10, 10 (1) 10}
(???) emperadual = {10, 10 (1) 10, 2}
(???) emperatrial = {10, 10 (1) 10, 3}
hyperal = {10, 10 (1) 10, 10}
(???) hyperadual = {10, 10 (1) 10, 10, 2}
(???) trideca-hyperal = {10, 10 (1) 10, 10, 10}
(???) deux tridecal = {10, 10, 10 (1) 10, 10, 10} = {10, 3 (1) (1) 2}
deux tetradecal = {10, 10, 10, 10 (1) 10, 10, 10, 10} = {10, 4 (1) (1) 2}
diteral / (???) deux iteral / (???) deux superdecal = {10, 10, 10, 10 (1) 10, 10, 10, 10} = {10, 4 (1) (1) 2}
diteral = {10, 10, 10, 10, 10, 10, 10, 10, 10, 10 (1) 10, 10, 10, 10, 10, 10, 10, 10, 10, 10} = {10, 10 (1)(1) 2}
admiral = {10, 10 (1)(1) 10}
(???) hypero-admiral = {10, 10 (1)(1) 10, 10}
(???) trideca-admiral = {10, 10 (1)(1) 10, 10, 10}
dutridecal = {10, 10, 10 (1) 10, 10, 10 (1) 10, 10, 10} = {10, 3 (1)(1)(1) 2} = {10, 3 (2) 2}
(???) dutetradecal = {10, 10, 10, 10 (1) 10, 10, 10, 10 (1) 10, 10, 10, 10} = {10, 4 (1)(1)(1) 2}
(???) triteral = {10, 10 (1)(1)(1) 2}
(???) quadriteral = {10, 10 (1)(1)(1)(1) 2}
(???) quintiteral = {10, 10 (1)(1)(1)(1)(1) 2}
(???) sextiiteral = {10, 10 (1)(1)(1)(1)(1)(1) 2}
xappol = {10, 10 (1)(1)(1)(1)(1)(1)(1)(1)(1)(1) 2} = {10, 10 (2) 2}
xappolplex = {10, {10, 10 (2) 2} (2) 2}
grand xappol = {10, 10 (2) 3}
(???) tritridecal = {10, 3 (2)(2)(2) 2} = {10, 3 (3) 2}
(???) tritetradecal = {10, 4 (2)(2)(2)(2) 2} = {10, 4 (3) 2}
colossol = {10, 10 (2)(2)(2)(2)(2)(2)(2)(2)(2)(2) 2} = {10, 10 (3) 2}
terossol = {10, 10 (4) 2}
petossol = {10, 10 (5) 2}
ectossol = {10, 10 (6) 2}
zettossol = {10, 10 (7) 2}
yottossol = {10, 10 (8) 2}
xennossol / (???) ronnossol = {10, 10 (9) 2}
dimendecal / (???) quettossol = {10, 10 (10) 2}
gongulus / (???) hectossol = {10, 10 (100) 2}
(???) duladecal = {10, 10 (0, 2) 2}
(???) triladecal = {10, 10 (0, 3) 2}
(???) tetladecal = {10, 10 (0, 4) 2}
(???) squarediladecal = {10, 10 (0, 0, 1) 2}
(???) squarediduladecal = {10, 10 (0, 0, 2) 2}
(???) cubiculadecal = {10, 10 (0, 0, 0, 1) 2}
(???) quarticuladecal = {10, 10 (0, 0, 0, 0, 1) 2}
(???) quinticuladecal = {10, 10 (0, 0, 0, 0, 0, 1) 2}
(???) trimendecal = {10, 10 (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1) 2} = {10, 10 ((1) 1) 2}
(???) quadramendecal = {10, 10 ((10) 1) 2} = {10, 10 ((0, 1) 1) 2}
(???) quintamendecal = {10, 10 (((1) 1) 1) 2}
(???) sextamendecal = {10, 10 (((0, 1) 1) 1) 2}
(???) septamendecal = {10, 10 ((((1) 1) 1) 1) 2}
(???) octamendecal = {10, 10 ((((0, 1) 1) 1) 1) 2}
(???) nonamendecal = {10, 10 (((((1) 1) 1) 1) 1) 2}
(???) decamendecal / (???) tetrational decal / (???) deckertrix = {10, 10 (((((0, 1) 1) 1) 1) 1) 2}