Solve 500!/495!*5!*{left(1/100right)}^5*{left(99/100right)}^495

$$\frac{ 500 ! }{ 495 ! \times 5 ! } \times { \left( \frac{ 1 }{ 100 } \right) }^{ 5 } \times { \left( \frac{ 99 }{ 100 } \right) }^{ 495 }$$

Evaluate

$$\frac{4408776126833744412117672541703874593750193307641718610522828417018283141525575368867512174076298528019923975274683105680146695727050257945097399532680365866945003491451955390848260997409424651262564362020383474735312994176562161286422436928688315111935218587580220854287117213388900296012348824271092658537198330305293187601390921182448069725034890191073715416697433000138281442936326158820119403897590448962440244456603669500581422515326694472450591540966440381561587203596443497941205758306654313185328377856883546070864234060154439651460959743748588745128936198243278714763826010271388704223758215770130521104282068591784895657296555656329408987661621512700150760083059397195730914607499790668378491211941727807687804647802678486528776002631464735866866948996114076547552732103370477837024609284637201893092597960484310120708002256824732190508866905632889919340722645967381756195748168545057374677919045777460413479026098827879758104186208848548640161085557935804394610065982812341974741628781}{25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 0.176351045$$

Solution Steps

The factorial of 500 is 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{495!\times 5!}\times \left(\frac{1}{100}\right)^{5}\times \left(\frac{99}{100}\right)^{495}$$

The factorial of 495 is 39835527935427442653307246390889133574455058929474360918831440169865373173062205245987407819877230158625954248105449553737789484754202879130453683311034798251040647448239996323595729529242460558022987116647853214200309640883549364452499131740748918231314884434143823158375186224673641496062809972380056937780444997576203214305328732152335729333031277824713798129156112852590636201781658170402000138642530440170821847233900697242790032037350027852544137918297862391191896981741518799468846174738258138349655578686063236119130723929973173232037676743659319972210894275877710333185091850615091699690800778651674399080909618893555520041340693021809886928098043362394126080750337167664977655745225761742519841258652832147366990072007520590506718330245094485979644081447888376081078472943701147302371285456158635432103502841496876705880085878159883750361223277928135652117374579120356599205611267455058317952893096761242338655156781065342979004276319051014016381377369519365969606362756724961345364788510720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{39835527935427442653307246390889133574455058929474360918831440169865373173062205245987407819877230158625954248105449553737789484754202879130453683311034798251040647448239996323595729529242460558022987116647853214200309640883549364452499131740748918231314884434143823158375186224673641496062809972380056937780444997576203214305328732152335729333031277824713798129156112852590636201781658170402000138642530440170821847233900697242790032037350027852544137918297862391191896981741518799468846174738258138349655578686063236119130723929973173232037676743659319972210894275877710333185091850615091699690800778651674399080909618893555520041340693021809886928098043362394126080750337167664977655745225761742519841258652832147366990072007520590506718330245094485979644081447888376081078472943701147302371285456158635432103502841496876705880085878159883750361223277928135652117374579120356599205611267455058317952893096761242338655156781065342979004276319051014016381377369519365969606362756724961345364788510720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times 5!}\times \left(\frac{1}{100}\right)^{5}\times \left(\frac{99}{100}\right)^{495}$$

The factorial of 5 is 120.

$$\frac{1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{39835527935427442653307246390889133574455058929474360918831440169865373173062205245987407819877230158625954248105449553737789484754202879130453683311034798251040647448239996323595729529242460558022987116647853214200309640883549364452499131740748918231314884434143823158375186224673641496062809972380056937780444997576203214305328732152335729333031277824713798129156112852590636201781658170402000138642530440170821847233900697242790032037350027852544137918297862391191896981741518799468846174738258138349655578686063236119130723929973173232037676743659319972210894275877710333185091850615091699690800778651674399080909618893555520041340693021809886928098043362394126080750337167664977655745225761742519841258652832147366990072007520590506718330245094485979644081447888376081078472943701147302371285456158635432103502841496876705880085878159883750361223277928135652117374579120356599205611267455058317952893096761242338655156781065342979004276319051014016381377369519365969606362756724961345364788510720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000\times 120}\times \left(\frac{1}{100}\right)^{5}\times \left(\frac{99}{100}\right)^{495}$$

Multiply 39835527935427442653307246390889133574455058929474360918831440169865373173062205245987407819877230158625954248105449553737789484754202879130453683311034798251040647448239996323595729529242460558022987116647853214200309640883549364452499131740748918231314884434143823158375186224673641496062809972380056937780444997576203214305328732152335729333031277824713798129156112852590636201781658170402000138642530440170821847233900697242790032037350027852544137918297862391191896981741518799468846174738258138349655578686063236119130723929973173232037676743659319972210894275877710333185091850615091699690800778651674399080909618893555520041340693021809886928098043362394126080750337167664977655745225761742519841258652832147366990072007520590506718330245094485979644081447888376081078472943701147302371285456158635432103502841496876705880085878159883750361223277928135652117374579120356599205611267455058317952893096761242338655156781065342979004276319051014016381377369519365969606362756724961345364788510720000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and 120 to get 4780263352251293118396869566906696028934607071536923310259772820383844780767464629518488938385267619035114509772653946448534738170504345495654441997324175790124877693788799558831487543509095266962758453997742385704037156906025923734299895808889870187757786132097258779005022346960836979527537196685606832533653399709144385716639447858280287519963753338965655775498733542310876344213798980448240016637103652820498621668068083669134803844482003342305296550195743486943027637808982255936261540968590976601958669442327588334295686871596780787844521209239118396665307313105325239982211022073811003962896093438200927889709154267226662404960883162617186431371765203487295129690040460119797318689427091409102380951038339857684038808640902470860806199629411338317557289773746605129729416753244137676284554254739036251852420340979625204705610305379186050043346793351376278254084949494442791904673352094606998154347171611349080638618813727841157480513158286121681965765284342323916352763530806995361443774621286400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{4780263352251293118396869566906696028934607071536923310259772820383844780767464629518488938385267619035114509772653946448534738170504345495654441997324175790124877693788799558831487543509095266962758453997742385704037156906025923734299895808889870187757786132097258779005022346960836979527537196685606832533653399709144385716639447858280287519963753338965655775498733542310876344213798980448240016637103652820498621668068083669134803844482003342305296550195743486943027637808982255936261540968590976601958669442327588334295686871596780787844521209239118396665307313105325239982211022073811003962896093438200927889709154267226662404960883162617186431371765203487295129690040460119797318689427091409102380951038339857684038808640902470860806199629411338317557289773746605129729416753244137676284554254739036251852420340979625204705610305379186050043346793351376278254084949494442791904673352094606998154347171611349080638618813727841157480513158286121681965765284342323916352763530806995361443774621286400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\times \left(\frac{1}{100}\right)^{5}\times \left(\frac{99}{100}\right)^{495}$$

Divide 1220136825991110068701238785423046926253574342803192842192413588385845373153881997605496447502203281863013616477148203584163378722078177200480785205159329285477907571939330603772960859086270429174547882424912726344305670173270769461062802310452644218878789465754777149863494367781037644274033827365397471386477878495438489595537537990423241061271326984327745715546309977202781014561081188373709531016356324432987029563896628911658974769572087926928871281780070265174507768410719624390394322536422605234945850129918571501248706961568141625359056693423813008856249246891564126775654481886506593847951775360894005745238940335798476363944905313062323749066445048824665075946735862074637925184200459369692981022263971952597190945217823331756934581508552332820762820023402626907898342451712006207714640979456116127629145951237229913340169552363850942885592018727433795173014586357570828355780158735432768888680120399882384702151467605445407663535984174430480128938313896881639487469658817504506926365338175055478128640000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 by 4780263352251293118396869566906696028934607071536923310259772820383844780767464629518488938385267619035114509772653946448534738170504345495654441997324175790124877693788799558831487543509095266962758453997742385704037156906025923734299895808889870187757786132097258779005022346960836979527537196685606832533653399709144385716639447858280287519963753338965655775498733542310876344213798980448240016637103652820498621668068083669134803844482003342305296550195743486943027637808982255936261540968590976601958669442327588334295686871596780787844521209239118396665307313105325239982211022073811003962896093438200927889709154267226662404960883162617186431371765203487295129690040460119797318689427091409102380951038339857684038808640902470860806199629411338317557289773746605129729416753244137676284554254739036251852420340979625204705610305379186050043346793351376278254084949494442791904673352094606998154347171611349080638618813727841157480513158286121681965765284342323916352763530806995361443774621286400000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 255244687600.

$$255244687600\times \left(\frac{1}{100}\right)^{5}\times \left(\frac{99}{100}\right)^{495}$$

Calculate \frac{1}{100} to the power of 5 and get \frac{1}{10000000000}.

$$255244687600\times \frac{1}{10000000000}\times \left(\frac{99}{100}\right)^{495}$$

Multiply 255244687600 and \frac{1}{10000000000} to get \frac{255244687600}{10000000000}.

$$\frac{255244687600}{10000000000}\times \left(\frac{99}{100}\right)^{495}$$

Reduce the fraction \frac{255244687600}{10000000000} to lowest terms by extracting and canceling out 400.

$$\frac{638111719}{25000000}\times \left(\frac{99}{100}\right)^{495}$$

Calculate \frac{99}{100} to the power of 495 and get \frac{6909097569533501095468319618345505724445398106913185542863895306424051336887569947398994836633455603437873823587751889697149874357738065526888402957978532074169607111465626273584016402321275424284386731377963416991113109735196951125767425262861087044124978039433594627788237208959486757227771308602299244933939742149279016142612044995914061445147805209127832075902422033622425045819172863083116961056141407367634074836045550670385701716483747060678243931399166768102541623430745201438943888611853425599488759517490613694346262366879426722236642928271606848720069029547596687789126797515199222071892736654364000333117324541386295488637712444722252448809236667067308256225677305255274452352597822558370051204061538019940054803793187328265908250200095033620385443816169871262860684279911301608652338956083647623924295865320583652700479955963216200561373651300846771223022540928106283839849317271443771553612613996610229123571540029779265195075047428409068539745088016169774512581836492399499}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{638111719}{25000000}\times \frac{6909097569533501095468319618345505724445398106913185542863895306424051336887569947398994836633455603437873823587751889697149874357738065526888402957978532074169607111465626273584016402321275424284386731377963416991113109735196951125767425262861087044124978039433594627788237208959486757227771308602299244933939742149279016142612044995914061445147805209127832075902422033622425045819172863083116961056141407367634074836045550670385701716483747060678243931399166768102541623430745201438943888611853425599488759517490613694346262366879426722236642928271606848720069029547596687789126797515199222071892736654364000333117324541386295488637712444722252448809236667067308256225677305255274452352597822558370051204061538019940054803793187328265908250200095033620385443816169871262860684279911301608652338956083647623924295865320583652700479955963216200561373651300846771223022540928106283839849317271443771553612613996610229123571540029779265195075047428409068539745088016169774512581836492399499}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply \frac{638111719}{25000000} times \frac{6909097569533501095468319618345505724445398106913185542863895306424051336887569947398994836633455603437873823587751889697149874357738065526888402957978532074169607111465626273584016402321275424284386731377963416991113109735196951125767425262861087044124978039433594627788237208959486757227771308602299244933939742149279016142612044995914061445147805209127832075902422033622425045819172863083116961056141407367634074836045550670385701716483747060678243931399166768102541623430745201438943888611853425599488759517490613694346262366879426722236642928271606848720069029547596687789126797515199222071892736654364000333117324541386295488637712444722252448809236667067308256225677305255274452352597822558370051204061538019940054803793187328265908250200095033620385443816169871262860684279911301608652338956083647623924295865320583652700479955963216200561373651300846771223022540928106283839849317271443771553612613996610229123571540029779265195075047428409068539745088016169774512581836492399499}{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{638111719\times 6909097569533501095468319618345505724445398106913185542863895306424051336887569947398994836633455603437873823587751889697149874357738065526888402957978532074169607111465626273584016402321275424284386731377963416991113109735196951125767425262861087044124978039433594627788237208959486757227771308602299244933939742149279016142612044995914061445147805209127832075902422033622425045819172863083116961056141407367634074836045550670385701716483747060678243931399166768102541623430745201438943888611853425599488759517490613694346262366879426722236642928271606848720069029547596687789126797515199222071892736654364000333117324541386295488637712444722252448809236667067308256225677305255274452352597822558370051204061538019940054803793187328265908250200095033620385443816169871262860684279911301608652338956083647623924295865320583652700479955963216200561373651300846771223022540928106283839849317271443771553612613996610229123571540029779265195075047428409068539745088016169774512581836492399499}{25000000\times 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Do the multiplications in the fraction \frac{638111719\times 6909097569533501095468319618345505724445398106913185542863895306424051336887569947398994836633455603437873823587751889697149874357738065526888402957978532074169607111465626273584016402321275424284386731377963416991113109735196951125767425262861087044124978039433594627788237208959486757227771308602299244933939742149279016142612044995914061445147805209127832075902422033622425045819172863083116961056141407367634074836045550670385701716483747060678243931399166768102541623430745201438943888611853425599488759517490613694346262366879426722236642928271606848720069029547596687789126797515199222071892736654364000333117324541386295488637712444722252448809236667067308256225677305255274452352597822558370051204061538019940054803793187328265908250200095033620385443816169871262860684279911301608652338956083647623924295865320583652700479955963216200561373651300846771223022540928106283839849317271443771553612613996610229123571540029779265195075047428409068539745088016169774512581836492399499}{25000000\times 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{4408776126833744412117672541703874593750193307641718610522828417018283141525575368867512174076298528019923975274683105680146695727050257945097399532680365866945003491451955390848260997409424651262564362020383474735312994176562161286422436928688315111935218587580220854287117213388900296012348824271092658537198330305293187601390921182448069725034890191073715416697433000138281442936326158820119403897590448962440244456603669500581422515326694472450591540966440381561587203596443497941205758306654313185328377856883546070864234060154439651460959743748588745128936198243278714763826010271388704223758215770130521104282068591784895657296555656329408987661621512700150760083059397195730914607499790668378491211941727807687804647802678486528776002631464735866866948996114076547552732103370477837024609284637201893092597960484310120708002256824732190508866905632889919340722645967381756195748168545057374677919045777460413479026098827879758104186208848548640161085557935804394610065982812341974741628781}{25000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{3 ^ {990} \cdot 7 \cdot 11 ^ {495} \cdot 31 \cdot 71 \cdot 83 \cdot 499}{2 ^ {996} \cdot 5 ^ {998}} = NaN$$