SRL Archive - Mathematics

hello everybody, i love math and do it in competitions at my highschool and am relatively new here, and theres this problem that stumped me. hoping some of you guys can help.

its simply this.

"simplify 1994^1994" (1994 raised to the 1994 power)

cant do it on a calculator

"x^x" ?

I'm not sure what exactly you mean by simplifying it? Anyway you do it will still get you the same answer. You could split it up into something like this though..

(Y^N) * (Y^N) = (Y^M).. In this case Y = 1994, M = 1994, and N = M/2. You could keep expanding it infinitely, but you'd still get (Y^M) in the end.

simplify as in 4.487x10^6579 (this is the answer)

11111001010

Shift Right 1

1111001010
S = Square, X = multiple by 1994.

the binary above becomes
S1994S1994S1994S1994SSS1994SS1994S
1994^2 = …
Result * 1994 = ….
That squared^2… and so on..


The result of 1994 ^ 1994 is both of the below in two different forms.

4.4870098966106959081161009800253e+6579

OR

4.4870098966106959081161009800253 * 10 ^ 6579

From: Brandon
11111001010

Shift Right 1

1111001010
S = Square, X = multiple by 1994.

the binary above becomes
S8S8S8S8SSS8SS8S
1994^2 = …
Result * 1994 = ….
That squared^2… and so on..


The result of 1994 ^ 1994 is both of the below in two different forms.

5.7734320919198422404919208157297 e+1800

OR

5.7734320919198422404919208157297 * (10 ^ 1800)

how does one do binary? how does one square such big numbers on a calculator? and also my answer sheet said the answer was 4.487x10^6579

From: martini0072
how does one do binary? how does one square such big numbers on a calculator? and also my answer sheet said the answer was 4.487x10^6579

Check my edit.. I accidentally missed an S. lol

K it goes like this:

Convert the powered number to binary.

Example: 2 ^ 6.. Convert the 6 to binary.
Example: 1994 ^ 1994.. Convert 1994 to binary.

Now you got some binary crap.
For every 0, replace it with S.
For every 1 Replace it with S1994.

S means square the previous value and 1994 means multiple the previous by that.

thus starting out we'd do:

1994 * 1994 = X;
X * X = Y.. Finally we hit 1994

Y * 1994 = Z
Z * Z = Alpha.
Alpha * 1994 = Beta
Beta * Beta = Iunno.. keep going till u eliminated all the S's and the 1994's. Finally you get your answer.

Also calculators can only do this in scientific notation.

C++:
int main()
{
          cout<<setprecision(15)<< pow(1994.0, 1994.0);   //these are doubles and hold the decimals no matter what.
}

The value in the end may be truncated.


Ohh and if you like cool tricks like that, wait till you hear about the taylor series for calculating sine of an angle manually!

sin x = x - x3/3! + x5/5! - x7/7! + … y

From: Brandon
11111001010

Shift Right 1

1111001010
S = Square, X = multiple by 1994.

the binary above becomes
S1994S1994S1994S1994SSS1994SS1994S
1994^2 = …
Result * 1994 = ….
That squared^2… and so on..


The result of 1994 ^ 1994 is both of the below in two different forms.

4.4870098966106959081161009800253e+6579

OR

4.4870098966106959081161009800253 * 10 ^ 6579

I get a similar answer:

44870098966106959081161009800253338947743890921828970724198046394957853401152290625970247254851884106552202576882314825133608035110428624408566397437346366730240998403312072561637865799536669837993265728462849395329238939149398219490416842049124576638110622781621145926049347325765917225920221099448336969005166200487822520499664369595012342967891371756200235250533622023316085094143563282683681202522556310689191655749482397549363849372897780029070323040732185754530557827398459801999780758598456175983868299475161580916768301578010437637239378741244622245051863899282838123230826352801876924976208163423480093293837163992400412067358479262062562272273823876446204680495773196684564500303864941045810943474839101497825573976438618787835274674732858791421602880320589889729888442755243038741791353473510012050471582684660622265937021390831671582865012381681926579323273361845038699379560493532702600649918162231848394292437376255673048943668522372411082185923260510924928166916491743522982300415662983403837566772979601812439539892097172987690035896594576186294788498775729800017545294761945109453643925954977167566463887797010257860166419782431296918368646873158898308836385884618984089231046166449588797548167619081358551455418897615243703952823112693328466990667154072088296855368267640557450917641621558032687015753513362416309088616787371103672974610027712469281027507053783885408922862011896725187807624589704696483700358867781826670805572969398081206769192748619018028322022579524286917711409431930362184982800315888426767171053827406981598176958147571956280570140037750878204458801231200809873070477226003117095773094204445147420845174495553487296078632332057243812211584249297935146824226612214942280866836898398912442565316675854641457453916034747826478977071073241906754357762414985348964176348799466311506216209953609638734561405201650978399529729887809358144397016570924523882145463454342730043827205632028531916411790387506947231047862769974036303290077697630519957872183620792461137114352319609267851420732917453816050979495317958745633332103174825075498539100139334792641586210581035144017674114188203279088417578370068923087344282399600807866667485715693101490372493295184027645586885766373144669060672570429057164304605685929875434173501766644553531640459498876996169850647369536797480373292221695672195125021624468484022345801312116483083505912645425207226545040035508076344699045266500880962425410888876340111886251526079328931981720291698739664759842704996684663823707099045109730536458671973678189931501382252264237213299985350236500198577131481988864207011099260699311026642579449096910949408024618445636210535139374211896583878356885290649327061592679372737894022722594924135635252527126591660131460279837669336371627936920915244765641190360005194714966387330220929577370596679457732677420266486403031784843185292701833750825204037847517017333453828440036404404650203147003309361782309639363462235016954301074155659218275992453633044185718851127090309583694155789665220638957646660125444898758914204566449623317728392430643359625804270459151453984890290435657865862018907574313072050571939402859734073259286666994509389985601841905183129432063977759129945793433709116898665914504996321702782872117636065308815121268510839930683620885474134395207048089929467935568464616588922028049318513873073224540068322714141236465930796140591967993064745336102059310160730463263320038824431312594937501235862773682160348592150107285594105545687810705880327847883902923301109632011686069737361435883992493837327171944409423641858349294178670814454992575114892638090132538360231889765808462753095682830431177755785470029360921784590622051027320886195851559832721867989429434036583774369665853287265378652223516284334520725525443315250204988390794234294272095455761148622856374215048213028980819140295708986016984108152712874548579487722007402422223656209809589603577227459373417477744255785399072485535377716437124274607591180112906429719996550064433922137658957842601858023187967082607283057954544804736088420903586235101239565948284082792379752822540209556374914411063844765746838786509727628873128152550452061422215829551263292979841003216703320873867089505530260578884563181156698771589436951230530958966558628302976108940160111325077146865749213644067427840418694714783931802961632824380978319060959598979674675551108479448186742201244484481211185047076745866407181570217458694872984649507422624083363945956204019572838290587039422610417592994448939329331620434000933672696460699221799320468135863832449874737501889910402717500392243666171949948201374608867453827028182225525296835954829126432650098981415970276767050110153737606750349797377896317169416854987554178760147159823392453445633090520290703952438318375009961432984575722923984926696800602725152927198295414348510201866777359814674421317367961554728122369902738208619401934714586202754713991695284747808323934658203981189641788909618044165499445955448451184119597177871958289604271019708285419020811207205572019990416333539050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or you could just say 2^(2*997) * 997^(2*997) but basically finding out what is it that they're looking for is probably best place to start… by the way what i wrote is factored version of your answer, and you can write it even nicer like this:

2^(997*2) * 997^(2*997)

and then it looks cool :P

use wolfram alpha :) or mathematica

1994^1994=10^x
log(1994^1994)=x
1994*log(1994)=x
1994*log(1994)=~6579.651957

1994^1994=~10^0.651957 * 10^6579 = 4.4870096*10^6579

From: doorsftw
use wolfram alpha :) or mathematica

I used MAPLE and gave him an exact answer to his question, not sure why this is still being commented on. :duh:

Why would you guys do this via binary and such when it's easily solvable with a logarithm…