frac{(-27)^{3}(32)^{-5}(-8)^{5}(25^{2})^-6}{(-72)^4(-50^3)^4} eching

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

Baholash

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

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 2 va -6 ni ko‘paytirib, -12 ni oling.

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

3 daraja ko‘rsatkichini -27 ga hisoblang va -19683 ni qiymatni oling.

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

-5 daraja ko‘rsatkichini 32 ga hisoblang va \frac{1}{33554432} ni qiymatni oling.

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

-\frac{19683}{33554432} hosil qilish uchun -19683 va \frac{1}{33554432} ni ko'paytirish.

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

5 daraja ko‘rsatkichini -8 ga hisoblang va -32768 ni qiymatni oling.

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

\frac{19683}{1024} hosil qilish uchun -\frac{19683}{33554432} va -32768 ni ko'paytirish.

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

-12 daraja ko‘rsatkichini 25 ga hisoblang va \frac{1}{59604644775390625} ni qiymatni oling.

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

\frac{19683}{61035156250000000000} hosil qilish uchun \frac{19683}{1024} va \frac{1}{59604644775390625} ni ko'paytirish.

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

4 daraja ko‘rsatkichini -72 ga hisoblang va 26873856 ni qiymatni oling.

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

3 daraja ko‘rsatkichini 50 ga hisoblang va 125000 ni qiymatni oling.

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

4 daraja ko‘rsatkichini -125000 ga hisoblang va 244140625000000000000 ni qiymatni oling.

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

6561000000000000000000000000 hosil qilish uchun 26873856 va 244140625000000000000 ni ko'paytirish.

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

\frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} ni yagona kasrga aylantiring.

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

400451660156250000000000000000000000000000000000 hosil qilish uchun 61035156250000000000 va 6561000000000000000000000000 ni ko'paytirish.

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

\frac{19683}{400451660156250000000000000000000000000000000000} ulushini 6561 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

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

Omil

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