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

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

Arvuta

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

Lahenduse etapid

Astme tõstmiseks mõnda teise astmesse korrutage astendajad. Korrutage 2 ja -6, et saada -12.

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

Arvutage 3 aste -27 ja leidke -19683.

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

Arvutage -5 aste 32 ja leidke \frac{1}{33554432}.

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

Korrutage -19683 ja \frac{1}{33554432}, et leida -\frac{19683}{33554432}.

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

Arvutage 5 aste -8 ja leidke -32768.

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

Korrutage -\frac{19683}{33554432} ja -32768, et leida \frac{19683}{1024}.

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

Arvutage -12 aste 25 ja leidke \frac{1}{59604644775390625}.

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

Korrutage \frac{19683}{1024} ja \frac{1}{59604644775390625}, et leida \frac{19683}{61035156250000000000}.

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

Arvutage 4 aste -72 ja leidke 26873856.

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

Arvutage 3 aste 50 ja leidke 125000.

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

Arvutage 4 aste -125000 ja leidke 244140625000000000000.

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

Korrutage 26873856 ja 244140625000000000000, et leida 6561000000000000000000000000.

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

Avaldage \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} ühe murdarvuna.

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

Korrutage 61035156250000000000 ja 6561000000000000000000000000, et leida 400451660156250000000000000000000000000000000000.

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

Taandage murd \frac{19683}{400451660156250000000000000000000000000000000000} vähimale ühiskordsele, eraldades ja taandades arvu 6561.

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

Lahuta teguriteks

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