Solved in head in under one minute. Just divide 2016 by 2 as often as possible. You get 63, which is 64-1.

(4)+(4)=8 (2^2)+(2^2).(1^1)+(1^2) (1^2).(n ➖ 2m+1). 2^31^1^2 (mn ➖ 2mn+1).

(2x+2x ➖}/x^2 =4x^2/x^2 =4x (x ➖ 4x+4).

{30+30}=60 30^30 15^15 2^3^2^3 2^1^1^3 23 (x ➖ 3x+2).

it cant be 1*1*1+10 ?

3^(Log[3,1.6 recurring ]+3)+ 3^(Log[3,1.6 recurring ]+3)=90 Input interpretation 3^(log(3, 1.6^_ (repeating decimal)) + 3) + 3^(log(3, 1.6^_ (repeating decimal)) + 3) = 90 Result True m=Log[3,1.6 recurring ]+3=Log[3,5]+2

(2X)/Sqrt[X]=4 X=4

A perfect demonstration of how to turn a 10 second problem into 10 minutes of waffling.

2048 - 32 = 2016 = 2^11 - 2^5 which actually is easily doable in your head in less than 10 seconds, but your thumbnail said 2^k - 2^k = 2016 which is impossible to solve and made me klick as I really wanted to know how 11% of students can solve x - x != 0 Of course, I reported you for klick baiting, have a nice day

5^5^5^5 = 5^5^3125 = 5^(5^5)^625 = 5^3125^625 = (5^3125)^3125^624 > 9^9^9

Totally misleading video thumbnail!

6^6;2^3^2^3 1^1^2^3 2^3 (x ➖ 3x+2).

2¹⁰ < 2016 < 2¹¹ 2¹¹ - 2016 = 32 = 2⁵ k = 11, l = 5

81 9^9 3^2^3^2 1^1^3^1 3^1(x ➖ 3x+1).

n=1/25

By observation one solution is 2 Factorise the equation to obtain (a-2)(a^2+2a+5) = 0 Solving a^2+2a+5 by the quadratic formula we get -1+i or -1-i So the solutions are 2, -1+i or -1-i

It’s in my head. 5^5^5^5>9^9^9

Is lambert w function a part of pre-uni curriculum in the states? Why are entrance exams based on it?

9^9^9 has 369,693,100 digits in it starting with 42812477317574704803698711593056352133905548224144351417475372305352388747173504835319366529943203337506041753364763100078032613904733860832080206037470612809165574132086446019861999614520310524428581489598115147194935176779655930215939338501502396942623105296758165694333346314749255384948593377812087624957216504195220601804571301517864051014594079041948663327336671830654410760234823633427933884734491714907139283876367034707332216158426388470264465058580355824823115778277866180114720994362906904734383664886646950233817353314932888115176124859712015335756443987605995621733954850395053696554453295547762183338179903753742986603617541076696090471833992393314534254702269833306512825870352073623634333080916193999239914353995174262626192250444914889355346296338764247108036190948328339353383268116816840967521737160227124038642410944863124167336163160258473857727316993387556729418877537923876279151815197169574861839692092170993607802644764408395926434454851800780948395933285398270164750251095376500141286928505876878853669407158547929415017596380093739697517984175797277906741998154544863852633240819143167556841941071017167324488713374402297730006005442460032552018028477336157137560860266753519143348470953542806215894313422062980873500411731911584053164106252625074754678272488405835202922863455599567929527725263396995135064858726675736711246852441322863857060434188996170746314452550800737145968257096891089328244493643959798289039293282259176510085281196595293102425014976453521015904277017376315464270157898635643459316227465877112764899643433942816964327754334261729541367769029853728352359400523470156112205493670498819450718472655897640862284961892386930305105845538762363318365185801372996391839875674546223545518466903561896465332510475421097914918068229109709788923977779069205784142152023066355758778007098449184758158930039377455058531904329503778881515696050048886761833287926112263005693440963183056933626394245522332228665776967696500187914684795893593661376277432887880749995343487723228420791524924222135827589942713699184294180078697183907586300014964478603049885761354056286480888955690040960321405163881482921695209409793162683259577472717346258467570821694584319916190683318100067000700317312978238094247916447104001549862704401974269675191670641229965446110840033825885602487560194393309325081375366882008389237055409085567149541011014966373535641244452380523501480247762164849736829169686750716817770925914324452205695748119745922757870920113028347619768327749309081935870766006147889390839590582306585235104348020762430064635269587843905488576330726918299779363650131041050536175666439482255699172870771835361637377004418994697597459514274925639015903862060776034

27^3-81^3=-511758 final answer

27^3 - 81^3 = 3^9 - 3^12 = 3^9 -3^3 * 3^9 = 3^9 - 27*3^9 = -26*3^9 = -26*27^3

THUMBNAIL SAID 2^K -2^K = 2016

That"s so ridiculously easy that not even thinking is required. Solved it in my head even quicker than I could click on the video. 2^11=2048, which is 32 too much. 32 is 2^5. Done within a second.

(-9)^x=9 x=Ln(9)/(πi+Ln(9))

Log[-9,9]=Log[81*81^Ln(3/e)e^π^2,81*81^Ln(3/e)]-Log[81*81^Ln(3/e)e^π^2,9^π]i

Is 2/2 invalid?

Much quicker to use the function in Excel.

Great video. You nailed it. Greetings from Zimbabwe.

Terrible. Can be done with simple algebra. He's going to be a teacher.

5^5^5^5 = 5^5^3125 = 5^5^(5•625) = 5^(5^5)^625 = 5^3125^625 = 5^(3125•(3125^624)) = (5^3125)^3125^624 > 9^9^9

Literally clickbait channel showing off how to avoid the solution with 7 minutes of transferring the exponent

2^3^2^3^2^3^2^3vs3^2^3^2^3^2 1^1^1^1^1^1^2^3vs 1^1^1^1^1^3 (x ➖ 3x+2).(x ➖ 3x+1). 2^3>1^3. 5^5^5^5>9^9^9.

2^3^2^3^2^3^2^3vs3^2^3^2^3^2 1^1^1^1^1^1^2^3vs1^1^1^1^1^3 (x ➖ 3x+2).(x ➖ 3x+1). 2^3>1^3 5^5^5^5>9^9^9.

{108+108}=216 108^108 2^3^2^3 1^1^1^1^1^2 1^2 (k ➖ 2k+1).

2^3x 1^1^2x 1^2x (x ➖ 2x+1).4x^2 2^2x^2 1^1x^2 1x^2 (x ➖ 2x+1).

I thought that here would be a great solution with original idea but we just calculated 2^22 manually...

4:25 you pulled those numbers out of your posterior. 😀 The following are all the other pairs where one of the factors is odd. (7, 288), (3, 672), (9, 224), (21, 96) What missing is that you didn't make an argument that the even factor needed to be a power of 2. While it's clear after a second of reflection, your students won't catch this immediately.

Harvard: LOL. You made something extremely simple into prolonged torture. Ten minutes to do a two second problem.

5^5^5^5 has 1335740483872136983278553267576972270185117116755770623464509952108004698723634695141721494068939747755880776754895822228478283164306089959075181736358643875142011799147283547727738586021173064814703759351787200723048996452180837630041307409473692833759543038486957703064566010472360798193844897605589101209504209454546774958263097513767322005810705465510777633793402220923322988231124499380424439282894586348521178336279713878482570450648894133922805711795524395180721755577133072829011359247659895136301739079549270233908702418503761947271998797692094217571935828520680086265908877829725529753690673413222413335141457348022727623821406421253394216922437369408375365044138477385362978939070193348911232191623640567202579256688731508805134606143360451570066660431849665570707995072667117979943418700904329537790777733444534356826194248543340029979607298598979103744123795468203121816270562993465625073390799292310876206480054943499921701981053068932160917042995650473685207117931122905311184987597866153492828905534778648508346956438533483529463545400629688440184097561918277710690496615665576491722728848636579498113893073186293783290393447423502230550086959070687911995376710553095253124476796816498105591285423461097512139376745630443495554201011735746680320466221827426343772864901989905286630523156047116799565300979194648323188418359198350164206270055286819668314925659846493860937631657241157097013065082686784886418347324172663937544110210588867178098393563591187150255202650819735855907135915839072602897862107060170941999135561047873407607465254705064027127522840239126685623536275936529205915455897239794879202503708562622454151398263462216516157561411707580327491275675138797655162805648207735829835427209449101693854416217529432327740944907213968718451694468579092144757572479746480888506714440881805312510714171714259041497922832068414296939198127726510628452902194894972351788023966437996758286189291242980328184944824149703182726638329129225378609706224897759972026849700096019344671574560956468320222614748613869096068225240517303611151511470364192869101537259798067994825728472312203914722815403202457084423163900089648908404030178142145781926143847736767828712084990 digits in it

5^5^5^5>9^9^9 starts with 1111028808179997445286178274186057545167346520596272154733386745225196554833740184735209940181105736435094708289972419456976689991179452562053707112701792446960169652563779814592619323578023085550658659155080871559349042107149488827117610174023191438325536594465702574550196546311017038616447942986993387902926501749136556811438895541999393635347107457459918028531118844504297553238552680328428132001782293310

5^5^5^5>9^9^9 It’s in my head. 9^9^9 has 369693100 digits starting with 428124773175747048036987115930563521339055482241443514174753723053523887471735048353193665299432033375060417533647631000780326139047338608320802060374706128091655741320864460198619996145203105244285814895981151471949351767796559302159393385015023969426231052967581656943333463147492553849485933778120876249572165041952206018045713015178640510145940790419486633273366718306544107602348236334279338847344917149071392838763670347073322161584263884702644650585803558248231157782778661801147209943629069047343836648866469502338173533149328881151761248597120153357564439876059956217339548503950536965544532955477621833381799037537429866036175410766960904718339923933145342547022698333065128258703520736236343330809161939992399143539951742626261922504449148893553462963387642471080361909483283393533832681168168409675217371602271240386424109448631241673361631602584738577273169933875567294188775379238762791518151971695748618396920921709936078026447644083959264344548518007809483959332853982701647502510953765001412869285058768788536694071585479294150175963800937396975179841757972779067419981545448638526332408191431675568419410710171673244887133744...

2*(2^21-1)=2*(2*16*(256^2)-1)

2048 - 32 = 2016, K=11, L=5. 89% of those students are stupid.

2^K-2^L=2016 L=5 K=11 final answer

a³+a=10 -->a(a²+1)=2×5 =2(2²+1) Similar structure of both side means that x=2

5:45 a very silly problem and a very primitive method of explanation in addition to the horrible handwriting

4^11-2 = 2^11*2^11-2 = 2048*2048-2 = 4194304-2 = 4194302

2^2^2^2 1^1^1^2 1^2 (x ➖ 2x+1).

(a ➖ 2a+1) .

4^11^1 ➖ 2 4^1^1 ➖ 2.2^2 ➖ 2 1^1 ➖ 2 1 ➖2 ( x ➖ 2x+1).