2008 ^ 2008 what is the answer with explanation ??

Question

anonymous · Answer

u have to find out its value??!!!

amistre64 · Answer

it 2008 multiplied to itself 2008 times

zarkon · Answer

89027999306855883832575312188457428019416830186565994335819245332973943055603687971214824226960969317897631564472102911983097818077225257828840863826114361386623805433685171758298346788910271776077901001648294552183321225136426112888480722357021956643143385558570116884210030540319715361299378669373139782776966883158778839461089607838469055613877814474880973683584716510250923161012500000050960006616519690281927001040239363754925964752023836896200110296521098354692643755653069884089395474735559831230052993531891674548012675683431092783377246694436600567081715666091297819975066040367444736601741341371271360592960153577649750128242704186035058371307188280122814551055044278457310514827497507781330522711760595212727989376657971267012863912216854572363799814059962626865146837361671068694858864616637127392494877789331824541515147799192670022543112142114736904288604567333306919410046735792810155624790061319725472700513603144114630022956084999860195638358800796047789108279357704749520929930179871092240156296828484973492708332873638592300997859006328323208435701941187276259901999677854022448617296305562833131774242079134141660468770282540297647256217592248341747871156585819755514675476616660612421145011052077472256447129183879558327600526890626024469738520662909374843335523000617636261262624746130108903650883516266574799792594818386442969878646506680613156418336521103715629303486440388019217824132924356231738651827159260457743333842785633366503529951676765894304908845199473831669059608988468291948837368082607611769519276754618911606372551417418479442160174429295055733747475791324634277289954847856806927367294585194249258327775394481973819523551244887581595774117107609595073358544078590148843734090530249115444094776629599262161307032935936362503123253036832854933515096760126500295987273449955515681458392757502586114744547831683212701481047049473565001626741464303498507884858492928655266152471498963075364520374992457773325942024717106827734882591358534971043323752237673136861797816774884549362189649305237812597570135383364139534139910254555025406938195296065308914885749191743585573075571112037263102000128677338778409909833820535246793479438867974159658728835548595103827770456188303570848163572961742651821163502440092409405226782407040225061254938110630292624827294631751179749271334745930217451270410141076272389986680145442979941917889622778742332324941660891518300199178055577718133701478603049888939908187500150124085933930017789418470831067665701237398957952596624013382278517947321016484010916821056221855759614417867366707295726764248572705940223092446461833582290147738371279109350431740778345388396731687632417693550193918214315370186964076737539340666779127689215046883040429401787612102319589698220686901549112271039299460942099725594197533146582020511188940681523391660696093115395777753084983313114153785972401166876581512187271584585314899904570339433301944392767187557124972541448374249930102012092407898976150003843372169531412293437335370465677809114951848961883219909704571608040642095883397547769944280109417316715528400441716506243932363902559414432043776820186435565783402362744583554001545976131028719080881722830536680555282638972301554392142366476697299899727017176403360072176452948320872202436809637969111495317840206733240957711401294091115277083991511884693357009592139438429985431202747620665210366816442502324085125492741677103536419647510063464821919038000893396196362121157914119515695439110237959664405435185719140273170879795244644213072621524898253611357575747443000513812780088335148379982018428605086233280186282743026852778801999503547802318696531275004980513595414786522617242109290124935544013274182629499625971842648279786409255188353471371132749468568148357502506619427140160922163808743693342286338654321745287625420245426055515068241780468005388351731374453096301167755839318397714232258760723984202932054989504383689528775957592563585192776274523219147573933657603675831177906684127737248531197804533092567397436800377320740405308995956221480615570032054898021043224457693625500315603494974543552505274120125435975282439483851163117165862875291217841792842579658707383621804760821813329444532733498965524409899683568336262943696482589488522797534580105458608387725949767317795099917290443945770287590610877092700387303002217208139010327702951349951903933902089312923345024551437281426044435363963307515780006040280081067395782909391504221887966285847713569718001157783887592811467711012025815558965287509144619843467956218715487067733688873694087777992379516250773663007423123918932610391739894246266151788099151971909542836240328497239801304712642751259131044921058484283126289457595624425605790117735530805604974088956202494288617810792977843583956569511636112627351718484062833874146461477712330880633672751313443867727972936742907191467832498373601058243512859748764056713017843980095824421654927979851756668107966215927298971671840869814660198104326494890760154154650446222324760222495513516305865726935164059973802335028741856348305409584183007083635368602858031352796647655569722132753621242883794643473562172268243032986681931167205561065430070779144299489325666543420532367959611685600781672189649381178538547980232892681181137324801281744171308593149309018194683355161652423835663224527847961125066924920513004697053757546899540925824564774005668707853262529002032851543634349522593439155757957139976622957140232790286797457443045612419612658520698570828852989865451275447235732626372503207327585965177989476104585473821947709915130162482904419936021707821505713954563913552475855658992296262151939583578957097201121374129267158728334928501178351035412209141426372675408800428059663203002634567301093452634038468051302270047114921065218485717423123327439113323454165560596344887298853973233531481322456842695885691289808619575290744584109322405577022059906484957177336242664393414697585459788901474141560422559245933296215001254463642220597977380102225172902164032378508517574279570750299552274482891493789829332610956260349177475572474100986214296292147601768931978023804687627313993557589566125257841503340496280593967696484278413822779051678315313064608398621513859991839849330846118769412468568399796325619209609220218142162603609667036270970164371009494106908623604048959102197438419086196661771339656058939995329194963411545876006842405409559129294764906851888130281201253784401546280847736160933315956218302192460660734410402020713291693500526333221742062367096941950558052479701790612215270080143682487922043969248973698389825577640893497231071210952384637013559655127848205017664388584986513864922439110971234153049491254642913860063871369216

zarkon · Answer

:)

anonymous · Answer

nice

anonymous · Answer

ok but can we know it's last digit without calculator ??

cwtan · Answer

wow which powerful calculator calculates that

zarkon · Answer

I used Mathematica

zarkon · Answer

yes...do $$2008^{2008} mod 10$$

anonymous · Answer

can u explain for me plz :P and really thank u for ur help :D

anonymous · Answer

what is the mod 10 ??

zarkon · Answer

http://en.wikipedia.org/wiki/Modular_arithmetic

anonymous · Answer

Thank u zarkon sooooooooooo much :D

anonymous · Answer

last digit of 2008 is 8
if u multiply it again with 2008, its last digit will be 4 as 8*8=64
applying this process, u can get 2,6,8
so, 8 comes every 5th time 
2008=5*401+3
so, last digit is the 3rd term, that is 6

anonymous · Answer

whats the part u cant get, @suzan998 ?

anonymous · Answer

something ending with 8
make it square its last digit will be 4. got it?
again, multiply with 8, last digit is 2, as 8*4=32
so on.. u can get, at the power 5, last digit 8 is repeated
obviously after 5, the results will come in cycle and repeated after every 5 power.
2008=5*401
so, at the power 2005, last digit will be 8
at 2006..............4
2007...................2
2008..................6

got it?

anonymous · Answer

so, 8 comes every 5th time 2008=5*401+3 so, last digit is the 3rd term, that is 6

anonymous · Answer

yeah.. exactly

anonymous · Answer

Ok i got it really thanks aloooooot for ur help :D

anonymous · Answer

welcome :)

yash2651995 · Answer

you can do it with binomial expantion if you wish it can tell you the last digit too. if you know about binomial theorem, then that'd be another way to do it :)