n^n^n for n=1 to n=5:

1

16

7625597484987

1340780792994259709957402499820584612747936582059239337772356144372176403007354697680187429816690342
7690031858186486050853753882811946569946433649006084096

1911012597945477520356404559703964599198081048990094337139512789246520530242615803012059386519739850
2655864401557944622353592127886738069722884101469159866020879618967571957018392816603380476112259755
3362610100148265112341314776825241149309444717696528275628519673751439535754247909321920664188301178
7169122552421070050709064674382870851449950256586194461543183511379849133691779928127433840431549236
8555267835963741021053315460313537253257486369091597786903282664591829838152302869365728736914226481
3129174376213632573032164528297948686257624536221801767322494056764281936007872071383707235530544635
6153946401185348493792719514594505508232749221605848912910945189959948686199543147666938013037176163
5925944797461642200508850794698044871332051331607391342305401988725700383298012460501970134673971759
0902738949392381731578699684589979478106804282243609378394633526542281570430283244238551508231649096
7285712171708123232790481817268327510112746782317410985888683708522000711733492253913322300756147180
4290075276777933523062006182860124552542430610068948054465847048206509826643193609603887362585107470
7434063628697657670269925864995355797631817390255089133122329474393034395616132833407283166349825814
5226862004307799084688103804187368324800903873596212919633602583120781673673742533322879296907205490
5956214068888259912445818423795978634764843156737609236250903715117989414242622702200662864868678687
1018298087280256069310194928083082504419842479679205890881711232719230145558291674679519743054802640
4646854002733993860798594465961501752586965811447568510041568687730903712482535343839285397598749458
4970500382250124892840018265900562512861876299380444073401423470620557853053250349181895897071993056
6218851296318750174353596028220103821161604854512103931331225633226076643623668829685020883949614283
0484739113991669622649948563685234712873294796680884509405893951104650944137909502276545653133018670
6335213230284605194343813998105614006525953007317907727110657834941746426847209561346473277485842382
7489966875505250439421823219135722305406671537337424854364566378204570165459321815405354839361425066
4498585403307466468541890148134347714650315037954175778622811776585876941680908203125

For each number, there are line-breaks after every 100 digits. Well, on a Mac anyways.
For 6^6^6 to 8^8^8, there is an additional line-break (a blank line) after every 100 line-breaks:
i.e., there are ten thousand digits in each full block or, if you will, "page".

6^6^6

7^7^7

8^8^8

For 9^9^9, I've expanded the number into 33 "volumes". Volumes whose numbers are divisible by five contain 1200 pages; the rest (except for the last) contain 1100 pages. Volume 33 contains 1169 full pages and a final part-page. All of this in trying to accomodate James Joyce in Ulysses (chapter 17) wherein is stated: "Because some years previously in 1886 when occupied with the problem of the quadrature of the circle he had learned of the existence of a number computed to a relative degree of accuracy to be of such magnitude and of so many places, e.g. the 9th power of the 9th power of 9, that, the result having been obtained, 33 closely printed volumes of 1000 pages each of innumerable quires and reams of India paper would have to be requisitioned in order to contain the complete tale of its printed integers of units, tens, hundreds, thousands, tens of thousands, hundreds of thousands, millions, tens of millions, hundreds of millions, billions, the nucleus of the nebula of every digit of every series containing succinctly the potentiality of being raised to the utmost kinetic elaboration of any power of any of its powers". I took a loose interpretation of "1000 pages" in order to maintain the 10000-digits-per-page structure already established.