(399/400)^400=0.3674191122606848364914267362776647644916308848958141976070306042356918633581746556597872381854544286500903218560796364547216767797141826339122965080650512687406560397402506673790453327061611541981634390542348352855327644936991090211656166738962045478653097864592844375848437033413460881985855494328166826134866909017764014572121368740178597188756358348928740954271735937024969260917738002538330439371829641137795242938074915229597391603003707264770636496005778457125708433024464645462711204056577587914112520298471092541765033339003188329313085669421725855835808295149191833573530372097250455290711643188634831385212119214398095934838767040346565365538758061324055035803961315929762253728460117709450665900892226471217693090004828195838808860911505292256400306391090826007286223065078379124336141749549199594056472601553903106514833696017720838547917943827184128685811263764653769986001246143301797952237047995345250244388334153354935119702227519950075637425159723348021225474770244832697527964149261243126192989497503846333236878121832793397339872861537052484407353111813123535938007378404891223504321584653879492921141803456195951024252181733335823161720201967461547484737375147486505225439078236716878633242459370316598360061499810338942231788083639789790179809791249744412262564518137565041305046489956494505693654457663994872031374662380449123134555687555131893097031888813791031518685862714008720344032233939909975232055670400758290491257470767998285522192308485481349646123128776722094628997952806180909854495412874172811516684387258895352035460921667243960886395370835089124739170074462890625

asked by guest
on Nov 19, 2024 at 2:13 am



You asked:

Investigate the equation: \({\left( \frac{399}{400} \right)}^{400} = 0.3674191122606848364914267362776647644916308848958141976070306042356918633581746556597872381854544286500903218560796364547216767797141826339122965080650512687406560397402506673790453327061611541981634390542348352855327644936991090211656166738962045478653097864592844375848437033413460881985855494328166826134866909017764014572121368740178597188756358348928740954271735937024969260917738002538330439371829641137795242938074915229597391603003707264770636496005778457125708433024464645462711204056577587914112520298471092541765033339003188329313085669421725855835808295149191833573530372097250455290711643188634831385212119214398095934838767040346565365538758061324055035803961315929762253728460117709450665900892226471217693090004828195838808860911505292256400306391090826007286223065078379124336141749549199594056472601553903106514833696017720838547917943827184128685811263764653769986001246143301797952237047995345250244388334153354935119702227519950075637425159723348021225474770244832697527964149261243126192989497503846333236878121832793397339872861537052484407353111813123535938007378404891223504321584653879492921141803456195951024252181733335823161720201967461547484737375147486505225439078236716878633242459370316598360061499810338942231788083639789790179809791249744412262564518137565041305046489956494505693654457663994872031374662380449123134555687555131893097031888813791031518685862714008720344032233939909975232055670400758290491257470767998285522192308485481349646123128776722094628997952806180909854495412874172811516684387258895352035460921667243960886395370835089124739170074462890625\).

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)}^{400} = \frac{244995594347014991222958215138333011751757203118178294234932011689377523986696900110669212533689399568942321228856793317550599918513137477271035729707827593432149673556370786782994924137072788733699608799153839423284795994770975961685671176166212997482933110138150992459534552374123392122359030366452836998978794659321648229646376253275046508913620579383829230444934815850586481838801751892233061821701406458598943012324815532940529958748035006271088420050691763623205282074493356794130751007347696890098148700288930348605346204642616049981083106041444146894547477527223197590668057508782733885210186998173362906719136498412899145111162071410830579149240732529070523431448824937622319993238372127489787591438931298761839337241381635758226916717440669427540163937731640079334348297063758118244031014865621722779405177216303665783841189715991327702534543032259733291392942396208148449287461516833605707185385673542002379041520028962016826775605336035959198042143461705203238668835017387975522845460596904317611613911748203801259044697567840001}{666801443287985427407985179072125779714475832231590816039625781176403723781763207152143220087155429074292991059343324044588880165411936508036335605233083004609515757951401455846307828591181402472896501613588660198169074803747646129116387737600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\]

The right-hand side of the equation is:

\[0.3674191122606848364914267362776647644916308848958141976070306042356918633581746556597872381854544286500903218560796364547216767797141826339122965080650512687406560397402506673790453327061611541981634390542348352855327644936991090211656166738962045478653097864592844375848437033413460881985855494328166826134866909017764014572121368740178597188756358348928740954271735937024969260917738002538330439371829641137795242938074915229597391603003707264770636496005778457125708433024464645462711204056577587914112520298471092541765033339003188329313085669421725855835808295149191833573530372097250455290711643188634831385212119214398095934838767040346565365538758061324055035803961315929762253728460117709450665900892226471217693090004828195838808860911505292256400306391090826007286223065078379124336141749549199594056472601553903106514833696017720838547917943827184128685811263764653769986001246143301797952237047995345250244388334153354935119702227519950075637425159723348021225474770244832697527964149261243126192989497503846333236878121832793397339872861537052484407353111813123535938007378404891223504321584653879492921141803456195951024252181733335823161720201967461547484737375147486505225439078236716878633242459370316598360061499810338942231788083639789790179809791249744412262564518137565041305046489956494505693654457663994872031374662380449123134555687555131893097031888813791031518685862714008720344032233939909975232055670400758290491257470767998285522192308485481349646123128776722094628997952806180909854495412874172811516684387258895352035460921667243960886395370835089124739170074462890625 = \frac{244995594347014991222958215138333011751757203118178294234932011689377523986696900110669212533689399568942321228856793317550599918513137477271035729707827593432149673556370786782994924137072788733699608799153839423284795994770975961685671176166212997482933110138150992459534552374123392122359030366452836998978794659321648229646376253275046508913620579383829230444934815850586481838801751892233061821701406458598943012324815532940529958748035006271088420050691763623205282074493356794130751007347696890098148700288930348605346204642616049981083106041444146894547477527223197590668057508782733885210186998173362906719136498412899145111162071410830579149240732529070523431448824937622319993238372127489787591438931298761839337241381635758226916717440669427540163937731640079334348297063758118244031014865621722779405177216303665783841189715991327702534543032259733291392942396208148449287461516833605707185385673542002379041520028962016826775605336035959198042143461705203238668835017387975522845460596904317611613911748203801259044697567840001}{666801443287985427407985179072125779714475832231590816039625781176403723781763207152143220087155429074292991059343324044588880165411936508036335605233083004609515757951401455846307828591181402472896501613588660198169074803747646129116387737600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\]

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