Solve 99!99!99!99^2

$$99 ! 99 ! 99 ! { 99 }^{ 2 }$$

Evaluate

$$7966753014094285054026977985004077669771518718722657700745178743219223780153879357979271456626386973623814573920465448117270650138204018176286892198674344533537135967882408759817401972186005323677702569348336428374525717553346088245569459041661042280701786582927380814680368727345559196366654179269065341601201341447362986637975629729823630595486864320303041640495299859144583374035148217649267743857311744000000000000000000000000000000000000000000000000000000000000000000$$

Solution Steps

Multiply 99! and 99! to get \left(99!\right)^{2}.

$$\left(99!\right)^{2}\times 99!\times 99^{2}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\left(99!\right)^{3}\times 99^{2}$$

The factorial of 99 is 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000.

$$933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000^{3}\times 99^{2}$$

Calculate 933262154439441526816992388562667004907159682643816214685929638952175999932299156089414639761565182862536979208272237582511852109168640000000000000000000000 to the power of 3 and get 812851037046656979290580347413945278009541752752031190770857947476708884823373059685672018837505047813877622071264712592314115920641160919935403754583649069843601261900051908970248135107234498895796609463150334493880799668742586291763030205250590988746228607583652771623341365916290092476956859429554672135618951275111007717373291473301054034842043089511584699570992741469705476383547415329993647980544000000000000000000000000000000000000000000000000000000000000000000.

$$812851037046656979290580347413945278009541752752031190770857947476708884823373059685672018837505047813877622071264712592314115920641160919935403754583649069843601261900051908970248135107234498895796609463150334493880799668742586291763030205250590988746228607583652771623341365916290092476956859429554672135618951275111007717373291473301054034842043089511584699570992741469705476383547415329993647980544000000000000000000000000000000000000000000000000000000000000000000\times 99^{2}$$

Calculate 99 to the power of 2 and get 9801.

$$812851037046656979290580347413945278009541752752031190770857947476708884823373059685672018837505047813877622071264712592314115920641160919935403754583649069843601261900051908970248135107234498895796609463150334493880799668742586291763030205250590988746228607583652771623341365916290092476956859429554672135618951275111007717373291473301054034842043089511584699570992741469705476383547415329993647980544000000000000000000000000000000000000000000000000000000000000000000\times 9801$$

Multiply 812851037046656979290580347413945278009541752752031190770857947476708884823373059685672018837505047813877622071264712592314115920641160919935403754583649069843601261900051908970248135107234498895796609463150334493880799668742586291763030205250590988746228607583652771623341365916290092476956859429554672135618951275111007717373291473301054034842043089511584699570992741469705476383547415329993647980544000000000000000000000000000000000000000000000000000000000000000000 and 9801 to get 7966753014094285054026977985004077669771518718722657700745178743219223780153879357979271456626386973623814573920465448117270650138204018176286892198674344533537135967882408759817401972186005323677702569348336428374525717553346088245569459041661042280701786582927380814680368727345559196366654179269065341601201341447362986637975629729823630595486864320303041640495299859144583374035148217649267743857311744000000000000000000000000000000000000000000000000000000000000000000.

$$7966753014094285054026977985004077669771518718722657700745178743219223780153879357979271456626386973623814573920465448117270650138204018176286892198674344533537135967882408759817401972186005323677702569348336428374525717553346088245569459041661042280701786582927380814680368727345559196366654179269065341601201341447362986637975629729823630595486864320303041640495299859144583374035148217649267743857311744000000000000000000000000000000000000000000000000000000000000000000$$

Factor

$$2^{285}\times 3^{148}\times 5^{66}\times 7^{48}\times 11^{29}\times 13^{21}\times 17^{15}\times 19^{15}\times 23^{12}\times 29^{9}\times 31^{9}\times 37^{6}\times 41^{6}\times 43^{6}\times 47^{6}\times 53^{3}\times 59^{3}\times 61^{3}\times 67^{3}\times 71^{3}\times 73^{3}\times 79^{3}\times 83^{3}\times 89^{3}\times 97^{3}$$