(399/400)^800=0.13499680405442972633904699808895743895302511863786484511649527311199960319177609283852993876268699185968805070243357247275821073425615016834377272758484829200955147300549160972161110742547041772633379401164349792168370993642319728767311247795899821754862466326212699228637401183492059935684887213155975463377238065199891773880305215181651340202259491859164671055093101556614128064424381383096073421707844724045504763583479096665977563876292928147061953640545552259373979874109711421150509508865545628740707684884183111103778633878462157868374867874242150981589361115056285121582799697847550380605259641035862274790977763063574908114175940878389599028373844578270893902550144404105082053755472510004837599314027183273637757350595225384380001645877498960329126601943137714601467710569443048198121000408483735917145260618784770080585561656030179081839112713857794477303456374426743542913816361356783064663372140380943264408363397341055170754300389121011622455124361431595229116634330711263432177696797686843453406947192115975840985843530042103920690952247810730821898900667866004990756622135391401708227432687433321284974028600666725553928929132406170543404228375062793051239188667426772618780023485211958808147391496225141405889688164951064830751586508804628107907013122048887998493925413768559832454131748160712955232833893480585254837319373584106586586892804258706832675543168482021983315791400973672740580976612939652738283370178472012488645457642181756597650240686671015513228897545734666325981408916822403397909251877440409090524008388167450609577202716787967867452831461027578312617860482094310440792539885106619134122631463209563958302600669431385520615202240264487356893009779999584711441745639062012214761884977933918162570617766137042434199838928239611297584405062722145816123332697291795013099933077142336977004560788579289425374643204707532993512393038865297046626474126668366748400619481417051368488570894615457434278291328059419288551597291494005704411754326822243574497028733275618629295445704350048293185141475349329613439296674020718975223747379084390412780643575825458756839509309671047046656256852581259187828825193197879270534183882735292178956911534220482990877917339819925755868886051661407317283564299138286713225887257254656594895547113294326077519614546141117798179928318205118754756158003907697094336285009006774774627665575678186834202358254504160122714363633963858984614337437683168182281740110410110442695692368089864834457263942172140485661133816532177916278630059703925971288080235029477029649125732351820906996989047678434537852897325770270620460285063659936119919549974252146584802850656912066347975489477131892912028803024935500779295399183707960166035576514306244432298353608865676221988035700084309955710487846797506003188005760364001425488198146285445475182889921696252080234268722243538277353457816326061112414579479490555259432962709416048340828716238242276875332619497940715152882644212089237603200252299423516046418326621911134550784630788952023275058858066024926431101698106962842124688835005837268891172934417025337969189707412650892462409139944774228100116226361909888555378556889501547353929522351606147075438746894306130119645104059600271284580230712890625

asked by guest
on Nov 19, 2024 at 6:32 am



You asked:

Investigate the equation: \({\left( \frac{399}{400} \right)}^{800} = 0.13499680405442972633904699808895743895302511863786484511649527311199960319177609283852993876268699185968805070243357247275821073425615016834377272758484829200955147300549160972161110742547041772633379401164349792168370993642319728767311247795899821754862466326212699228637401183492059935684887213155975463377238065199891773880305215181651340202259491859164671055093101556614128064424381383096073421707844724045504763583479096665977563876292928147061953640545552259373979874109711421150509508865545628740707684884183111103778633878462157868374867874242150981589361115056285121582799697847550380605259641035862274790977763063574908114175940878389599028373844578270893902550144404105082053755472510004837599314027183273637757350595225384380001645877498960329126601943137714601467710569443048198121000408483735917145260618784770080585561656030179081839112713857794477303456374426743542913816361356783064663372140380943264408363397341055170754300389121011622455124361431595229116634330711263432177696797686843453406947192115975840985843530042103920690952247810730821898900667866004990756622135391401708227432687433321284974028600666725553928929132406170543404228375062793051239188667426772618780023485211958808147391496225141405889688164951064830751586508804628107907013122048887998493925413768559832454131748160712955232833893480585254837319373584106586586892804258706832675543168482021983315791400973672740580976612939652738283370178472012488645457642181756597650240686671015513228897545734666325981408916822403397909251877440409090524008388167450609577202716787967867452831461027578312617860482094310440792539885106619134122631463209563958302600669431385520615202240264487356893009779999584711441745639062012214761884977933918162570617766137042434199838928239611297584405062722145816123332697291795013099933077142336977004560788579289425374643204707532993512393038865297046626474126668366748400619481417051368488570894615457434278291328059419288551597291494005704411754326822243574497028733275618629295445704350048293185141475349329613439296674020718975223747379084390412780643575825458756839509309671047046656256852581259187828825193197879270534183882735292178956911534220482990877917339819925755868886051661407317283564299138286713225887257254656594895547113294326077519614546141117798179928318205118754756158003907697094336285009006774774627665575678186834202358254504160122714363633963858984614337437683168182281740110410110442695692368089864834457263942172140485661133816532177916278630059703925971288080235029477029649125732351820906996989047678434537852897325770270620460285063659936119919549974252146584802850656912066347975489477131892912028803024935500779295399183707960166035576514306244432298353608865676221988035700084309955710487846797506003188005760364001425488198146285445475182889921696252080234268722243538277353457816326061112414579479490555259432962709416048340828716238242276875332619497940715152882644212089237603200252299423516046418326621911134550784630788952023275058858066024926431101698106962842124688835005837268891172934417025337969189707412650892462409139944774228100116226361909888555378556889501547353929522351606147075438746894306130119645104059600271284580230712890625\).

MathBot Answer:

This equation has no unknown quantities, so it is either true or false.

This equation is true because the left-hand side is equal to the right-hand side.

The left-hand side of the equation is:

\[{\left( \frac{399}{400} \right)}^{800} = \frac{60022841249447123923566272843461143856781226397182514707095153309123277333164323782871601153308476141346265932793028776969273388979760202338985411084213271405307050131069854395795605598150925355969698782332007351778645315518374778762934475460035193648243386918872842896133310582176165154461076378664900203900452879154477366122680821507433670116029545585408386594610912473847445231724797619119837553759409997359000361600110921226227391205670166473835551031287872199010435578684292011648445504864412652005056513923672930422218015437233550371171704716025490882657569554124170527729775932930556379162076710786947457995030004581422950306343028336977183289937755755155245023450956972955770206549558004223738460043817077907326289886699557805253814898655716468733688457591593329646840660004112397492641828403185954578479437965069766821697258073258048334960391711689873241638023692701617180584183107480453832201853098221328583554153246711920509581799390120039596622824526824891972509451939383674410889548522080783039162671760728173674788762101150436173618140954799222788482126346897585001186456332915383589545660670016257280131549535046094287430265722541287925003042124415798117718844206866554404397679686951920917185992035914940392026682101695547015991540086728647201322732780606715468955170407554535146126744826429406489660305705422233408142428744309845993158461292503427426351840365787869306591973238084164670898379142331212621387089271968272562645469998109851631634806540134445195832982701401097116597279020743281905490435034346924247243869327445815170776548225421165528016455864854707695382694949371906263791127906180377009082210309534257930338131863563565621052078421915390993684131491754244181403653987276344262363243738835296020082985098246339916249149420503620548425426730567401278987879479337861833071530739877009247579957679676069141459332857497537278346287796478199676984814778807963491248398830450959371545339075391588318276528976378791317489651489385404576036698780763499411076503101396095541562655896793640180912582219581392928145349410311433118665554101293329491660735680001}{444624164770940446200168140655173643158192345121378393194182230937536830697691522389847825761739694174859535211410493837451070564552839793163850167016128101195625850786204159767307056983450870390359307612750838272654055960654181736526850357888981139916270423292468503140298771616224874118777795788920970296904615320019153113668624689421488922059978838282657212902962202492026747406698147058185647650099603003896418433219360084164737751445119292467882465595389709572961606263646453760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\]

The right-hand side of the equation is:

\[0.13499680405442972633904699808895743895302511863786484511649527311199960319177609283852993876268699185968805070243357247275821073425615016834377272758484829200955147300549160972161110742547041772633379401164349792168370993642319728767311247795899821754862466326212699228637401183492059935684887213155975463377238065199891773880305215181651340202259491859164671055093101556614128064424381383096073421707844724045504763583479096665977563876292928147061953640545552259373979874109711421150509508865545628740707684884183111103778633878462157868374867874242150981589361115056285121582799697847550380605259641035862274790977763063574908114175940878389599028373844578270893902550144404105082053755472510004837599314027183273637757350595225384380001645877498960329126601943137714601467710569443048198121000408483735917145260618784770080585561656030179081839112713857794477303456374426743542913816361356783064663372140380943264408363397341055170754300389121011622455124361431595229116634330711263432177696797686843453406947192115975840985843530042103920690952247810730821898900667866004990756622135391401708227432687433321284974028600666725553928929132406170543404228375062793051239188667426772618780023485211958808147391496225141405889688164951064830751586508804628107907013122048887998493925413768559832454131748160712955232833893480585254837319373584106586586892804258706832675543168482021983315791400973672740580976612939652738283370178472012488645457642181756597650240686671015513228897545734666325981408916822403397909251877440409090524008388167450609577202716787967867452831461027578312617860482094310440792539885106619134122631463209563958302600669431385520615202240264487356893009779999584711441745639062012214761884977933918162570617766137042434199838928239611297584405062722145816123332697291795013099933077142336977004560788579289425374643204707532993512393038865297046626474126668366748400619481417051368488570894615457434278291328059419288551597291494005704411754326822243574497028733275618629295445704350048293185141475349329613439296674020718975223747379084390412780643575825458756839509309671047046656256852581259187828825193197879270534183882735292178956911534220482990877917339819925755868886051661407317283564299138286713225887257254656594895547113294326077519614546141117798179928318205118754756158003907697094336285009006774774627665575678186834202358254504160122714363633963858984614337437683168182281740110410110442695692368089864834457263942172140485661133816532177916278630059703925971288080235029477029649125732351820906996989047678434537852897325770270620460285063659936119919549974252146584802850656912066347975489477131892912028803024935500779295399183707960166035576514306244432298353608865676221988035700084309955710487846797506003188005760364001425488198146285445475182889921696252080234268722243538277353457816326061112414579479490555259432962709416048340828716238242276875332619497940715152882644212089237603200252299423516046418326621911134550784630788952023275058858066024926431101698106962842124688835005837268891172934417025337969189707412650892462409139944774228100116226361909888555378556889501547353929522351606147075438746894306130119645104059600271284580230712890625 = \frac{60022841249447123923566272843461143856781226397182514707095153309123277333164323782871601153308476141346265932793028776969273388979760202338985411084213271405307050131069854395795605598150925355969698782332007351778645315518374778762934475460035193648243386918872842896133310582176165154461076378664900203900452879154477366122680821507433670116029545585408386594610912473847445231724797619119837553759409997359000361600110921226227391205670166473835551031287872199010435578684292011648445504864412652005056513923672930422218015437233550371171704716025490882657569554124170527729775932930556379162076710786947457995030004581422950306343028336977183289937755755155245023450956972955770206549558004223738460043817077907326289886699557805253814898655716468733688457591593329646840660004112397492641828403185954578479437965069766821697258073258048334960391711689873241638023692701617180584183107480453832201853098221328583554153246711920509581799390120039596622824526824891972509451939383674410889548522080783039162671760728173674788762101150436173618140954799222788482126346897585001186456332915383589545660670016257280131549535046094287430265722541287925003042124415798117718844206866554404397679686951920917185992035914940392026682101695547015991540086728647201322732780606715468955170407554535146126744826429406489660305705422233408142428744309845993158461292503427426351840365787869306591973238084164670898379142331212621387089271968272562645469998109851631634806540134445195832982701401097116597279020743281905490435034346924247243869327445815170776548225421165528016455864854707695382694949371906263791127906180377009082210309534257930338131863563565621052078421915390993684131491754244181403653987276344262363243738835296020082985098246339916249149420503620548425426730567401278987879479337861833071530739877009247579957679676069141459332857497537278346287796478199676984814778807963491248398830450959371545339075391588318276528976378791317489651489385404576036698780763499411076503101396095541562655896793640180912582219581392928145349410311433118665554101293329491660735680001}{444624164770940446200168140655173643158192345121378393194182230937536830697691522389847825761739694174859535211410493837451070564552839793163850167016128101195625850786204159767307056983450870390359307612750838272654055960654181736526850357888981139916270423292468503140298771616224874118777795788920970296904615320019153113668624689421488922059978838282657212902962202492026747406698147058185647650099603003896418433219360084164737751445119292467882465595389709572961606263646453760000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\]

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