Solve 66.66^2-6.66^6/66.6/frac{66.6^66{666}}

$$66.66 ^ { 2 } - \frac { \frac { 6.66 ^ { 6 } } { 66.6 } } { \frac { 66.6 ^ { 66 } } { 666 } }$$

Evaluate

$$\frac{1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321782949703254463174340459747425080193484587}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000}\approx 4443.5556$$

Solution Steps

Calculate 66.66 to the power of 2 and get 4443.5556.

$$4443.5556-\frac{\frac{6.66^{6}}{66.6}}{\frac{66.6^{66}}{666}}$$

Divide \frac{6.66^{6}}{66.6} by \frac{66.6^{66}}{666} by multiplying \frac{6.66^{6}}{66.6} by the reciprocal of \frac{66.6^{66}}{666}.

$$4443.5556-\frac{6.66^{6}\times 666}{66.6\times 66.6^{66}}$$

Calculate 6.66 to the power of 6 and get 87266.061345623616.

$$4443.5556-\frac{87266.061345623616\times 666}{66.6\times 66.6^{66}}$$

Multiply 87266.061345623616 and 666 to get 58119196.856185328256.

$$4443.5556-\frac{58119196.856185328256}{66.6\times 66.6^{66}}$$

To multiply powers of the same base, add their exponents. Add 1 and 66 to get 67.

$$4443.5556-\frac{58119196.856185328256}{66.6^{67}}$$

Calculate 66.6 to the power of 67 and get 148858402649632927463208797392714560051860119787467131275832287954885460588330286425612870649752251167689898463923689419479.7996353420578908108193095036050596734614805576708229736997276614656.

$$4443.5556-\frac{58119196.856185328256}{148858402649632927463208797392714560051860119787467131275832287954885460588330286425612870649752251167689898463923689419479.7996353420578908108193095036050596734614805576708229736997276614656}$$

Expand \frac{58119196.856185328256}{148858402649632927463208797392714560051860119787467131275832287954885460588330286425612870649752251167689898463923689419479.7996353420578908108193095036050596734614805576708229736997276614656} by multiplying both numerator and the denominator by 10000000000000000000000000000000000000000000000000000000000000000000.

$$4443.5556-\frac{581191968561853282560000000000000000000000000000000000000000000000000000000}{1488584026496329274632087973927145600518601197874671312758322879548854605883302864256128706497522511676898984639236894194797996353420578908108193095036050596734614805576708229736997276614656}$$

Reduce the fraction \frac{581191968561853282560000000000000000000000000000000000000000000000000000000}{1488584026496329274632087973927145600518601197874671312758322879548854605883302864256128706497522511676898984639236894194797996353420578908108193095036050596734614805576708229736997276614656} to lowest terms by extracting and canceling out 2093964746436709975480187199116279808.

$$4443.5556-\frac{277555756156289135105907917022705078125}{710892592164909059141678510440371174922170148733908363116750960930081560508031164224921027761644306227517028673304170005271292512561385312843505975897632}$$

Convert decimal number 4443.5556 to fraction \frac{44435556}{10000}. Reduce the fraction \frac{44435556}{10000} to lowest terms by extracting and canceling out 4.

$$\frac{11108889}{2500}-\frac{277555756156289135105907917022705078125}{710892592164909059141678510440371174922170148733908363116750960930081560508031164224921027761644306227517028673304170005271292512561385312843505975897632}$$

Least common multiple of 2500 and 710892592164909059141678510440371174922170148733908363116750960930081560508031164224921027761644306227517028673304170005271292512561385312843505975897632 is 444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000. Convert \frac{11108889}{2500} and \frac{277555756156289135105907917022705078125}{710892592164909059141678510440371174922170148733908363116750960930081560508031164224921027761644306227517028673304170005271292512561385312843505975897632} to fractions with denominator 444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000.

$$\frac{1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321956422050852143883781652195564270867312712}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000}-\frac{173472347597680709441192448139190673828125}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000}$$

Since \frac{1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321956422050852143883781652195564270867312712}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000} and \frac{173472347597680709441192448139190673828125}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321956422050852143883781652195564270867312712-173472347597680709441192448139190673828125}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000}$$

Subtract 173472347597680709441192448139190673828125 from 1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321956422050852143883781652195564270867312712 to get 1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321782949703254463174340459747425080193484587.

$$\frac{1974306724320561108274835461541856125252492955349619635508920116403903204157625452978854682792506263840873854285388321782949703254463174340459747425080193484587}{444307870103068161963549069025231984326356342958692726947969350581300975317519477640575642351027691392198142920815106253294557820350865820527191234936020000}$$