frac{(53)^{4}+4+(40)^4}{(5^3)^2+2(44)^2+5194}=? eching

$$\frac { ( 53 ) ^ { 4 } + 4 + ( 40 ) ^ { 4 } } { ( 5 ^ { 3 } ) ^ { 2 } + 2 ( 44 ) ^ { 2 } + 5194 } = ?$$

Baholash

$$\frac{10450485}{24691}\approx 423,250779636$$

Yechim qadamlari

Daraja ko‘rsatkichini boshqa ko‘rsatkichga oshirish uchun, darajalarini ko‘paytiring. 3 va 2 ni ko‘paytirib, 6 ni oling.

$$\frac{53^{4}+4+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

4 daraja ko‘rsatkichini 53 ga hisoblang va 7890481 ni qiymatni oling.

$$\frac{7890481+4+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

7890485 olish uchun 7890481 va 4'ni qo'shing.

$$\frac{7890485+40^{4}}{5^{6}+2\times 44^{2}+5194}$$

4 daraja ko‘rsatkichini 40 ga hisoblang va 2560000 ni qiymatni oling.

$$\frac{7890485+2560000}{5^{6}+2\times 44^{2}+5194}$$

10450485 olish uchun 7890485 va 2560000'ni qo'shing.

$$\frac{10450485}{5^{6}+2\times 44^{2}+5194}$$

6 daraja ko‘rsatkichini 5 ga hisoblang va 15625 ni qiymatni oling.

$$\frac{10450485}{15625+2\times 44^{2}+5194}$$

2 daraja ko‘rsatkichini 44 ga hisoblang va 1936 ni qiymatni oling.

$$\frac{10450485}{15625+2\times 1936+5194}$$

3872 hosil qilish uchun 2 va 1936 ni ko'paytirish.

$$\frac{10450485}{15625+3872+5194}$$

19497 olish uchun 15625 va 3872'ni qo'shing.

$$\frac{10450485}{19497+5194}$$

24691 olish uchun 19497 va 5194'ni qo'shing.

$$\frac{10450485}{24691}$$

Omil

$$\frac{3 ^ {3} \cdot 5 \cdot 199 \cdot 389}{24691} = 423\frac{6192}{24691} = 423,25077963630474$$