Solve 1601.0035^105-1/0.0035

$$160 \frac{ { 1.0035 }^{ 105 } -1 }{ 0.0035 }$$

Evaluate

$$20260.274632809304207556705767869633801192292829492288437456557078166944227408668382765880878965994238036495037452724905107992402542634474492626391845362212358180170520453148784762229059788667332075139104680683690535440633984705661773393653131325776810174046984641678945432833496498824261385107099613419236047569910052935865913361725495178975957095722566067513671661217672229950148565791323562734760344028472900390625$$

Solution Steps

Calculate 1.0035 to the power of 105 and get 1.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875.

$$160\times \frac{1.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875-1}{0.0035}$$

Subtract 1 from 1.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875 to get 0.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875.

$$160\times \frac{0.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875}{0.0035}$$

Expand \frac{0.443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875}{0.0035} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$160\times \frac{443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875}{3500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Reduce the fraction \frac{443193507592703529540302938672148239401081405645143809569362186084901904974564620873003644227381123957048328944278357299237333805620129129526202321617298395335191230134912629666673760682877097889143667914889955730462763868415436351292986162247751367722557277789036726931343232735911780717799217804043545788540591782407972066854787745207040099061468931132726861567589136580030159499876685202934822882525622844696044921875}{3500000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 172563323017096332433815623655609487741013907680098782293498516082763671875.

$$160\times \frac{2568294929906948451789668839909529145644552164540122171135401415722815002907170118111070890715697115169490722959108751066787143036027669394880414605319225202084165052930180269490888143232004265186944834293147438657147418687244390217594774140472813252298741320553874136734254305260482912388082989769446877033815998675260453527172310984856304092401}{20282409603651670423947251286016000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Express 160\times \frac{2568294929906948451789668839909529145644552164540122171135401415722815002907170118111070890715697115169490722959108751066787143036027669394880414605319225202084165052930180269490888143232004265186944834293147438657147418687244390217594774140472813252298741320553874136734254305260482912388082989769446877033815998675260453527172310984856304092401}{20282409603651670423947251286016000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} as a single fraction.

$$\frac{160\times 2568294929906948451789668839909529145644552164540122171135401415722815002907170118111070890715697115169490722959108751066787143036027669394880414605319225202084165052930180269490888143232004265186944834293147438657147418687244390217594774140472813252298741320553874136734254305260482912388082989769446877033815998675260453527172310984856304092401}{20282409603651670423947251286016000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 160 and 2568294929906948451789668839909529145644552164540122171135401415722815002907170118111070890715697115169490722959108751066787143036027669394880414605319225202084165052930180269490888143232004265186944834293147438657147418687244390217594774140472813252298741320553874136734254305260482912388082989769446877033815998675260453527172310984856304092401 to get 410927188785111752286347014385524663303128346326419547381664226515650400465147218897771342514511538427118515673457400170685942885764427103180866336851076032333466408468828843118542102917120682429911173486903590185143586989959102434815163862475650120367798611288619861877480688841677265982093278363111500325410559788041672564347569757577008654784160.

$$\frac{410927188785111752286347014385524663303128346326419547381664226515650400465147218897771342514511538427118515673457400170685942885764427103180866336851076032333466408468828843118542102917120682429911173486903590185143586989959102434815163862475650120367798611288619861877480688841677265982093278363111500325410559788041672564347569757577008654784160}{20282409603651670423947251286016000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Reduce the fraction \frac{410927188785111752286347014385524663303128346326419547381664226515650400465147218897771342514511538427118515673457400170685942885764427103180866336851076032333466408468828843118542102917120682429911173486903590185143586989959102434815163862475650120367798611288619861877480688841677265982093278363111500325410559788041672564347569757577008654784160}{20282409603651670423947251286016000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to lowest terms by extracting and canceling out 160.

$$\frac{2568294929906948451789668839909529145644552164540122171135401415722815002907170118111070890715697115169490722959108751066787143036027669394880414605319225202084165052930180269490888143232004265186944834293147438657147418687244390217594774140472813252298741320553874136734254305260482912388082989769446877033815998675260453527172310984856304092401}{126765060022822940149670320537600000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$