---
id: 5900f3d01000cf542c50fee2
title: 'Problem 99: Largest exponential'
challengeType: 5
forumTopicId: 302216
dashedName: problem-99-largest-exponential
---

# --description--

Comparing two numbers written in index form like $2^{11}$ and $3^7$ is not difficult, as any calculator would confirm that $2^{11} = 2048 < 3^7 = 2187$.

However, confirming that $632382^{518061} < 519432^{525806}$ would be much more difficult, as both numbers contain over three million digits.

Using the 2D `baseExp` array of base/exponent pairs, determine pair with the greatest numerical value and return it.

# --hints--

`largestExponential(testArray1)` should return an array.

```js
assert(Array.isArray(largestExponential(_testArray1)));
```

`largestExponential(testArray1)` should return `[840237, 507276]`.

```js
assert.deepEqual(largestExponential(_testArray1), [840237, 507276]);
```

`largestExponential(testArray2)` should return `[895447, 504922]`.

```js
assert.deepEqual(largestExponential(_testArray2), [895447, 504922]);
```

# --seed--

## --after-user-code--

```js
const _testArray1 = [
  [492798,527927],[30125,670983],[895603,504906],[450785,531539],[840237,507276],[380711,538522],[63577,625673],[76801,615157],[502694,527123]
];
const _testArray2 = [
  [519432,525806],[632382,518061],[78864,613712],[466580,530130],[780495,510032],[525895,525320],[15991,714883],[960290,502358],[760018,511029],[166800,575487],[210884,564478],[555151,523163],[681146,515199],[563395,522587],[738250,512126],[923525,503780],[595148,520429],[177108,572629],[750923,511482],[440902,532446],[881418,505504],[422489,534197],[979858,501616],[685893,514935],[747477,511661],[167214,575367],[234140,559696],[940238,503122],[728969,512609],[232083,560102],[900971,504694],[688801,514772],[189664,569402],[891022,505104],[445689,531996],[119570,591871],[821453,508118],[371084,539600],[911745,504251],[623655,518600],[144361,582486],[352442,541775],[420726,534367],[295298,549387],[6530,787777],[468397,529976],[672336,515696],[431861,533289],[84228,610150],[805376,508857],[444409,532117],[33833,663511],[381850,538396],[402931,536157],[92901,604930],[304825,548004],[731917,512452],[753734,511344],[51894,637373],[151578,580103],[295075,549421],[303590,548183],[333594,544123],[683952,515042],[60090,628880],[951420,502692],[28335,674991],[714940,513349],[343858,542826],[549279,523586],[804571,508887],[260653,554881],[291399,549966],[402342,536213],[408889,535550],[40328,652524],[375856,539061],[768907,510590],[165993,575715],[976327,501755],[898500,504795],[360404,540830],[478714,529095],[694144,514472],[488726,528258],[841380,507226],[328012,544839],[22389,690868],[604053,519852],[329514,544641],[772965,510390],[492798,527927],[30125,670983],[895603,504906],[450785,531539],[840237,507276],[380711,538522],[63577,625673],[76801,615157],[502694,527123],[597706,520257],[310484,547206],[944468,502959],[121283,591152],[451131,531507],[566499,522367],[425373,533918],[40240,652665],[39130,654392],[714926,513355],[469219,529903],[806929,508783],[287970,550487],[92189,605332],[103841,599094],[671839,515725],[452048,531421],[987837,501323],[935192,503321],[88585,607450],[613883,519216],[144551,582413],[647359,517155],[213902,563816],[184120,570789],[258126,555322],[502546,527130],[407655,535678],[401528,536306],[477490,529193],[841085,507237],[732831,512408],[833000,507595],[904694,504542],[581435,521348],[455545,531110],[873558,505829],[94916,603796],[720176,513068],[545034,523891],[246348,557409],[556452,523079],[832015,507634],[173663,573564],[502634,527125],[250732,556611],[569786,522139],[216919,563178],[521815,525623],[92304,605270],[164446,576167],[753413,511364],[11410,740712],[448845,531712],[925072,503725],[564888,522477],[7062,780812],[641155,517535],[738878,512100],[636204,517828],[372540,539436],[443162,532237],[571192,522042],[655350,516680],[299741,548735],[581914,521307],[965471,502156],[513441,526277],[808682,508700],[237589,559034],[543300,524025],[804712,508889],[247511,557192],[543486,524008],[504383,526992],[326529,545039],[792493,509458],[86033,609017],[126554,589005],[579379,521481],[948026,502823],[404777,535969],[265767,554022],[266876,553840],[46631,643714],[492397,527958],[856106,506581],[795757,509305],[748946,511584],[294694,549480],[409781,535463],[775887,510253],[543747,523991],[210592,564536],[517119,525990],[520253,525751],[247926,557124],[592141,520626],[346580,542492],[544969,523902],[506501,526817],[244520,557738],[144745,582349],[69274,620858],[292620,549784],[926027,503687],[736320,512225],[515528,526113],[407549,535688],[848089,506927],[24141,685711],[9224,757964],[980684,501586],[175259,573121],[489160,528216],[878970,505604],[969546,502002],[525207,525365],[690461,514675],[156510,578551],[659778,516426],[468739,529945],[765252,510770],[76703,615230],[165151,575959],[29779,671736],[928865,503569],[577538,521605],[927555,503618],[185377,570477],[974756,501809],[800130,509093],[217016,563153],[365709,540216],[774508,510320],[588716,520851],[631673,518104],[954076,502590],[777828,510161],[990659,501222],[597799,520254],[786905,509727],[512547,526348],[756449,511212],[869787,505988],[653747,516779],[84623,609900],[839698,507295],[30159,670909],[797275,509234],[678136,515373],[897144,504851],[989554,501263],[413292,535106],[55297,633667],[788650,509637],[486748,528417],[150724,580377],[56434,632490],[77207,614869],[588631,520859],[611619,519367],[100006,601055],[528924,525093],[190225,569257],[851155,506789],[682593,515114],[613043,519275],[514673,526183],[877634,505655],[878905,505602],[1926,914951],[613245,519259],[152481,579816],[841774,507203],[71060,619442],[865335,506175],[90244,606469],[302156,548388],[399059,536557],[478465,529113],[558601,522925],[69132,620966],[267663,553700],[988276,501310],[378354,538787],[529909,525014],[161733,576968],[758541,511109],[823425,508024],[149821,580667],[269258,553438],[481152,528891],[120871,591322],[972322,501901],[981350,501567],[676129,515483],[950860,502717],[119000,592114],[392252,537272],[191618,568919],[946699,502874],[289555,550247],[799322,509139],[703886,513942],[194812,568143],[261823,554685],[203052,566221],[217330,563093],[734748,512313],[391759,537328],[807052,508777],[564467,522510],[59186,629748],[113447,594545],[518063,525916],[905944,504492],[613922,519213],[439093,532607],[445946,531981],[230530,560399],[297887,549007],[459029,530797],[403692,536075],[855118,506616],[963127,502245],[841711,507208],[407411,535699],[924729,503735],[914823,504132],[333725,544101],[176345,572832],[912507,504225],[411273,535308],[259774,555036],[632853,518038],[119723,591801],[163902,576321],[22691,689944],[402427,536212],[175769,572988],[837260,507402],[603432,519893],[313679,546767],[538165,524394],[549026,523608],[61083,627945],[898345,504798],[992556,501153],[369999,539727],[32847,665404],[891292,505088],[152715,579732],[824104,507997],[234057,559711],[730507,512532],[960529,502340],[388395,537687],[958170,502437],[57105,631806],[186025,570311],[993043,501133],[576770,521664],[215319,563513],[927342,503628],[521353,525666],[39563,653705],[752516,511408],[110755,595770],[309749,547305],[374379,539224],[919184,503952],[990652,501226],[647780,517135],[187177,570017],[168938,574877],[649558,517023],[278126,552016],[162039,576868],[658512,516499],[498115,527486],[896583,504868],[561170,522740],[747772,511647],[775093,510294],[652081,516882],[724905,512824],[499707,527365],[47388,642755],[646668,517204],[571700,522007],[180430,571747],[710015,513617],[435522,532941],[98137,602041],[759176,511070],[486124,528467],[526942,525236],[878921,505604],[408313,535602],[926980,503640],[882353,505459],[566887,522345],[3326,853312],[911981,504248],[416309,534800],[392991,537199],[622829,518651],[148647,581055],[496483,527624],[666314,516044],[48562,641293],[672618,515684],[443676,532187],[274065,552661],[265386,554079],[347668,542358],[31816,667448],[181575,571446],[961289,502320],[365689,540214],[987950,501317],[932299,503440],[27388,677243],[746701,511701],[492258,527969],[147823,581323],[57918,630985],[838849,507333],[678038,515375],[27852,676130],[850241,506828],[818403,508253],[131717,587014],[850216,506834],[904848,504529],[189758,569380],[392845,537217],[470876,529761],[925353,503711],[285431,550877],[454098,531234],[823910,508003],[318493,546112],[766067,510730],[261277,554775],[421530,534289],[694130,514478],[120439,591498],[213308,563949],[854063,506662],[365255,540263],[165437,575872],[662240,516281],[289970,550181],[847977,506933],[546083,523816],[413252,535113],[975829,501767],[361540,540701],[235522,559435],[224643,561577],[736350,512229],[328303,544808],[35022,661330],[307838,547578],[474366,529458],[873755,505819],[73978,617220],[827387,507845],[670830,515791],[326511,545034],[309909,547285],[400970,536363],[884827,505352],[718307,513175],[28462,674699],[599384,520150],[253565,556111],[284009,551093],[343403,542876],[446557,531921],[992372,501160],[961601,502308],[696629,514342],[919537,503945],[894709,504944],[892201,505051],[358160,541097],[448503,531745],[832156,507636],[920045,503924],[926137,503675],[416754,534757],[254422,555966],[92498,605151],[826833,507873],[660716,516371],[689335,514746],[160045,577467],[814642,508425],[969939,501993],[242856,558047],[76302,615517],[472083,529653],[587101,520964],[99066,601543],[498005,527503],[709800,513624],[708000,513716],[20171,698134],[285020,550936],[266564,553891],[981563,501557],[846502,506991],[334,1190800],[209268,564829],[9844,752610],[996519,501007],[410059,535426],[432931,533188],[848012,506929],[966803,502110],[983434,501486],[160700,577267],[504374,526989],[832061,507640],[392825,537214],[443842,532165],[440352,532492],[745125,511776],[13718,726392],[661753,516312],[70500,619875],[436952,532814],[424724,533973],[21954,692224],[262490,554567],[716622,513264],[907584,504425],[60086,628882],[837123,507412],[971345,501940],[947162,502855],[139920,584021],[68330,621624],[666452,516038],[731446,512481],[953350,502619],[183157,571042],[845400,507045],[651548,516910],[20399,697344],[861779,506331],[629771,518229],[801706,509026],[189207,569512],[737501,512168],[719272,513115],[479285,529045],[136046,585401],[896746,504860],[891735,505067],[684771,514999],[865309,506184],[379066,538702],[503117,527090],[621780,518717],[209518,564775],[677135,515423],[987500,501340],[197049,567613],[329315,544673],[236756,559196],[357092,541226],[520440,525733],[213471,563911],[956852,502490],[702223,514032],[404943,535955],[178880,572152],[689477,514734],[691351,514630],[866669,506128],[370561,539656],[739805,512051],[71060,619441],[624861,518534],[261660,554714],[366137,540160],[166054,575698],[601878,519990],[153445,579501],[279899,551729],[379166,538691],[423209,534125],[675310,515526],[145641,582050],[691353,514627],[917468,504026],[284778,550976],[81040,612235],[161699,576978],[616394,519057],[767490,510661],[156896,578431],[427408,533714],[254849,555884],[737217,512182],[897133,504851],[203815,566051],[270822,553189],[135854,585475],[778805,510111],[784373,509847],[305426,547921],[733418,512375],[732087,512448],[540668,524215],[702898,513996],[628057,518328],[640280,517587],[422405,534204],[10604,746569],[746038,511733],[839808,507293],[457417,530938],[479030,529064],[341758,543090],[620223,518824],[251661,556451],[561790,522696],[497733,527521],[724201,512863],[489217,528217],[415623,534867],[624610,518548],[847541,506953],[432295,533249],[400391,536421],[961158,502319],[139173,584284],[421225,534315],[579083,521501],[74274,617000],[701142,514087],[374465,539219],[217814,562985],[358972,540995],[88629,607424],[288597,550389],[285819,550812],[538400,524385],[809930,508645],[738326,512126],[955461,502535],[163829,576343],[826475,507891],[376488,538987],[102234,599905],[114650,594002],[52815,636341],[434037,533082],[804744,508880],[98385,601905],[856620,506559],[220057,562517],[844734,507078],[150677,580387],[558697,522917],[621751,518719],[207067,565321],[135297,585677],[932968,503404],[604456,519822],[579728,521462],[244138,557813],[706487,513800],[711627,513523],[853833,506674],[497220,527562],[59428,629511],[564845,522486],[623621,518603],[242689,558077],[125091,589591],[363819,540432],[686453,514901],[656813,516594],[489901,528155],[386380,537905],[542819,524052],[243987,557841],[693412,514514],[488484,528271],[896331,504881],[336730,543721],[728298,512647],[604215,519840],[153729,579413],[595687,520398],[540360,524240],[245779,557511],[924873,503730],[509628,526577],[528523,525122],[3509,847707],[522756,525555],[895447,504922],[44840,646067],[45860,644715],[463487,530404],[398164,536654],[894483,504959],[619415,518874],[966306,502129],[990922,501212],[835756,507474],[548881,523618],[453578,531282],[474993,529410],[80085,612879],[737091,512193],[50789,638638],[979768,501620],[792018,509483],[665001,516122],[86552,608694],[462772,530469],[589233,520821],[891694,505072],[592605,520594],[209645,564741],[42531,649269],[554376,523226],[803814,508929],[334157,544042],[175836,572970],[868379,506051],[658166,516520],[278203,551995],[966198,502126],[627162,518387],[296774,549165],[311803,547027],[843797,507118],[702304,514032],[563875,522553],[33103,664910],[191932,568841],[543514,524006],[506835,526794],[868368,506052],[847025,506971],[678623,515342],[876139,505726],[571997,521984],[598632,520198],[213590,563892],[625404,518497],[726508,512738],[689426,514738],[332495,544264],[411366,535302],[242546,558110],[315209,546555],[797544,509219],[93889,604371],[858879,506454],[124906,589666],[449072,531693],[235960,559345],[642403,517454],[720567,513047],[705534,513858],[603692,519870],[488137,528302],[157370,578285],[63515,625730],[666326,516041],[619226,518883],[443613,532186],[597717,520257],[96225,603069],[86940,608450],[40725,651929],[460976,530625],[268875,553508],[270671,553214],[363254,540500],[384248,538137],[762889,510892],[377941,538833],[278878,551890],[176615,572755],[860008,506412],[944392,502967],[608395,519571],[225283,561450],[45095,645728],[333798,544090],[625733,518476],[995584,501037],[506135,526853],[238050,558952],[557943,522972],[530978,524938],[634244,517949],[177168,572616],[85200,609541],[953043,502630],[523661,525484],[999295,500902],[840803,507246],[961490,502312],[471747,529685],[380705,538523],[911180,504275],[334149,544046],[478992,529065],[325789,545133],[335884,543826],[426976,533760],[749007,511582],[667067,516000],[607586,519623],[674054,515599],[188534,569675],[565185,522464],[172090,573988],[87592,608052],[907432,504424],[8912,760841],[928318,503590],[757917,511138],[718693,513153],[315141,546566],[728326,512645],[353492,541647],[638429,517695],[628892,518280],[877286,505672],[620895,518778],[385878,537959],[423311,534113],[633501,517997],[884833,505360],[883402,505416],[999665,500894],[708395,513697],[548142,523667],[756491,511205],[987352,501340],[766520,510705],[591775,520647],[833758,507563],[843890,507108],[925551,503698],[74816,616598],[646942,517187],[354923,541481],[256291,555638],[634470,517942],[930904,503494],[134221,586071],[282663,551304],[986070,501394],[123636,590176],[123678,590164],[481717,528841],[423076,534137],[866246,506145],[93313,604697],[783632,509880],[317066,546304],[502977,527103],[141272,583545],[71708,618938],[617748,518975],[581190,521362],[193824,568382],[682368,515131],[352956,541712],[351375,541905],[505362,526909],[905165,504518],[128645,588188],[267143,553787],[158409,577965],[482776,528754],[628896,518282],[485233,528547],[563606,522574],[111001,595655],[115920,593445],[365510,540237],[959724,502374],[938763,503184],[930044,503520],[970959,501956],[913658,504176],[68117,621790],[989729,501253],[567697,522288],[820427,508163],[54236,634794],[291557,549938],[124961,589646],[403177,536130],[405421,535899],[410233,535417],[815111,508403],[213176,563974],[83099,610879],[998588,500934],[513640,526263],[129817,587733],[1820,921851],[287584,550539],[299160,548820],[860621,506386],[529258,525059],[586297,521017],[953406,502616],[441234,532410],[986217,501386],[781938,509957],[461247,530595],[735424,512277],[146623,581722],[839838,507288],[510667,526494],[935085,503327],[737523,512167],[303455,548204],[992779,501145],[60240,628739],[939095,503174],[794368,509370],[501825,527189],[459028,530798],[884641,505363],[512287,526364],[835165,507499],[307723,547590],[160587,577304],[735043,512300],[493289,527887],[110717,595785],[306480,547772],[318593,546089],[179810,571911],[200531,566799],[314999,546580],[197020,567622],[301465,548487],[237808,559000],[131944,586923],[882527,505449],[468117,530003],[711319,513541],[156240,578628],[965452,502162],[992756,501148],[437959,532715],[739938,512046],[614249,519196],[391496,537356],[62746,626418],[688215,514806],[75501,616091],[883573,505412],[558824,522910],[759371,511061],[173913,573489],[891351,505089],[727464,512693],[164833,576051],[812317,508529],[540320,524243],[698061,514257],[69149,620952],[471673,529694],[159092,577753],[428134,533653],[89997,606608],[711061,513557],[779403,510081],[203327,566155],[798176,509187],[667688,515963],[636120,517833],[137410,584913],[217615,563034],[556887,523038],[667229,515991],[672276,515708],[325361,545187],[172115,573985],[13846,725685]
];
```

## --seed-contents--

```js
function largestExponential(baseExp) {

  return true;
}

// Only change code above this line

const testArray1 = [
  [492798,527927],[30125,670983],[895603,504906],[450785,531539],[840237,507276],[380711,538522],[63577,625673],[76801,615157],[502694,527123]
];

largestExponential(testArray1);
```

# --solutions--

```js
function largestExponential(baseExp) {
  let maximum = 0;
  let indexOfMaximum = 0;
  for (let i = 1; i < baseExp.length; i++) {
    const curValue = Math.log(baseExp[i][0]) * baseExp[i][1];
    if (curValue > maximum) {
      maximum = curValue;
      indexOfMaximum = i;
    }
  }

  return baseExp[indexOfMaximum];
}
```