Solve 0=135(1-(1/3)^180)/1-(frac{1{3})}

$$0 = \frac { 135 ( 1 - ( \frac { 1 } { 3 } ) ^ { 180 } ) } { 1 - ( \frac { 1 } { 3 } ) }$$

Verify

Solution Steps

Calculate \frac{1}{3} to the power of 180 and get \frac{1}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}.

$$0=\frac{135\left(1-\frac{1}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}\right)}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}.

$$0=\frac{135\left(\frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}-\frac{1}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}\right)}{1-\frac{1}{3}}$$

Since \frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601} and \frac{1}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601} have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{135\times \frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601-1}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}}{1-\frac{1}{3}}$$

Subtract 1 from 76177348045866392339289727720615561750424801402395196724001565744957137343033038019601 to get 76177348045866392339289727720615561750424801402395196724001565744957137343033038019600.

$$0=\frac{135\times \frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019600}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}}{1-\frac{1}{3}}$$

Express 135\times \frac{76177348045866392339289727720615561750424801402395196724001565744957137343033038019600}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601} as a single fraction.

$$0=\frac{\frac{135\times 76177348045866392339289727720615561750424801402395196724001565744957137343033038019600}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}}{1-\frac{1}{3}}$$

Multiply 135 and 76177348045866392339289727720615561750424801402395196724001565744957137343033038019600 to get 10283941986191962965804113242283100836307348189323351557740211375569213541309460132646000.

$$0=\frac{\frac{10283941986191962965804113242283100836307348189323351557740211375569213541309460132646000}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601}}{1-\frac{1}{3}}$$

Reduce the fraction \frac{10283941986191962965804113242283100836307348189323351557740211375569213541309460132646000}{76177348045866392339289727720615561750424801402395196724001565744957137343033038019601} to lowest terms by extracting and canceling out 27.

$$0=\frac{\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763}}{1-\frac{1}{3}}$$

Convert 1 to fraction \frac{3}{3}.

$$0=\frac{\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763}}{\frac{3}{3}-\frac{1}{3}}$$

Since \frac{3}{3} and \frac{1}{3} have the same denominator, subtract them by subtracting their numerators.

$$0=\frac{\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763}}{\frac{3-1}{3}}$$

Subtract 1 from 3 to get 2.

$$0=\frac{\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763}}{\frac{2}{3}}$$

Divide \frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763} by \frac{2}{3} by multiplying \frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763} by the reciprocal of \frac{2}{3}.

$$0=\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763}\times \frac{3}{2}$$

Multiply \frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763} times \frac{3}{2} by multiplying numerator times numerator and denominator times denominator.

$$0=\frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000\times 3}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763\times 2}$$

Do the multiplications in the fraction \frac{380886740229331961696448638603077808752124007011975983620007828724785686715165190098000\times 3}{2821383260958014531084804730393168953719437088977599878666724657220634716408631037763\times 2}.

$$0=\frac{1142660220687995885089345915809233426256372021035927950860023486174357060145495570294000}{5642766521916029062169609460786337907438874177955199757333449314441269432817262075526}$$

Reduce the fraction \frac{1142660220687995885089345915809233426256372021035927950860023486174357060145495570294000}{5642766521916029062169609460786337907438874177955199757333449314441269432817262075526} to lowest terms by extracting and canceling out 6.

$$0=\frac{190443370114665980848224319301538904376062003505987991810003914362392843357582595049000}{940461086986004843694934910131056317906479029659199959555574885740211572136210345921}$$

Compare 0 and \frac{190443370114665980848224319301538904376062003505987991810003914362392843357582595049000}{940461086986004843694934910131056317906479029659199959555574885740211572136210345921}.

$$\text{false}$$