ແກ້ frac{-27^332^-5-8^5{left(25^2right)}^-6}{{-72}^4{left(-{50}^3right)}^4}

$$\frac{ { -27 }^{ 3 } { 32 }^{ -5 } { -8 }^{ 5 } { \left( { 25 }^{ 2 } \right) }^{ -6 } }{ { -72 }^{ 4 } { \left(- { 50 }^{ 3 } \right) }^{ 4 } }$$

ປະເມີນ

$$\frac{3}{61035156250000000000000000000000000000000000}=4,9152 \cdot 10^{-44}$$

ຂັ້ນຕອນການແກ້

ເພື່ອຍົກເລກກຳລັງໃຫ້ສູງຂຶ້ນ, ໃຫ້ຄູນເລກກຳລັງນັ້ນ. ຄູນ 2 ກັບ -6 ເພື່ອໃຫ້ໄດ້ -12.

$$\frac{\left(-27\right)^{3}\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄຳນວນ -27 ກຳລັງ 3 ແລະ ໄດ້ -19683.

$$\frac{-19683\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄຳນວນ 32 ກຳລັງ -5 ແລະ ໄດ້ \frac{1}{33554432}.

$$\frac{-19683\times \frac{1}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄູນ -19683 ກັບ \frac{1}{33554432} ເພື່ອໃຫ້ໄດ້ -\frac{19683}{33554432}.

$$\frac{-\frac{19683}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄຳນວນ -8 ກຳລັງ 5 ແລະ ໄດ້ -32768.

$$\frac{-\frac{19683}{33554432}\left(-32768\right)\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄູນ -\frac{19683}{33554432} ກັບ -32768 ເພື່ອໃຫ້ໄດ້ \frac{19683}{1024}.

$$\frac{\frac{19683}{1024}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄຳນວນ 25 ກຳລັງ -12 ແລະ ໄດ້ \frac{1}{59604644775390625}.

$$\frac{\frac{19683}{1024}\times \frac{1}{59604644775390625}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄູນ \frac{19683}{1024} ກັບ \frac{1}{59604644775390625} ເພື່ອໃຫ້ໄດ້ \frac{19683}{61035156250000000000}.

$$\frac{\frac{19683}{61035156250000000000}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

ຄຳນວນ -72 ກຳລັງ 4 ແລະ ໄດ້ 26873856.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-50^{3}\right)^{4}}$$

ຄຳນວນ 50 ກຳລັງ 3 ແລະ ໄດ້ 125000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-125000\right)^{4}}$$

ຄຳນວນ -125000 ກຳລັງ 4 ແລະ ໄດ້ 244140625000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\times 244140625000000000000}$$

ຄູນ 26873856 ກັບ 244140625000000000000 ເພື່ອໃຫ້ໄດ້ 6561000000000000000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000}$$

ສະແດງ \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} ເປັນໜຶ່ງເສດສ່ວນ.

$$\frac{19683}{61035156250000000000\times 6561000000000000000000000000}$$

ຄູນ 61035156250000000000 ກັບ 6561000000000000000000000000 ເພື່ອໃຫ້ໄດ້ 400451660156250000000000000000000000000000000000.

$$\frac{19683}{400451660156250000000000000000000000000000000000}$$

ຫຼຸດເສດສ່ວນ \frac{19683}{400451660156250000000000000000000000000000000000} ເປັນຈຳນວນໜ້ອຍສຸດໂດຍແຍກ ແລະ ຍົກເລີກ 6561.

$$\frac{3}{61035156250000000000000000000000000000000000}$$

ຕົວປະກອບ

$$\frac{3}{2 ^ {34} \cdot 5 ^ {48}} = 4,9152000000000005 \times 10^{-44}$$