(5^{2}*5^3*5^4):(5^6-5^2) eching

$$( 5 ^ { 2 } \cdot 5 ^ { 3 } \cdot 5 ^ { 4 } ) : ( 5 ^ { 6 } - 5 ^ { 2 } )$$

Baholash

$$\frac{78125}{624}\approx 125,200320513$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 3 ni qo‘shib, 5 ni oling.

$$\frac{5^{5}\times 5^{4}}{5^{6}-5^{2}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va 4 ni qo‘shib, 9 ni oling.

$$\frac{5^{9}}{5^{6}-5^{2}}$$

9 daraja ko‘rsatkichini 5 ga hisoblang va 1953125 ni qiymatni oling.

$$\frac{1953125}{5^{6}-5^{2}}$$

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

$$\frac{1953125}{15625-5^{2}}$$

2 daraja ko‘rsatkichini 5 ga hisoblang va 25 ni qiymatni oling.

$$\frac{1953125}{15625-25}$$

15600 olish uchun 15625 dan 25 ni ayirish.

$$\frac{1953125}{15600}$$

\frac{1953125}{15600} ulushini 25 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{78125}{624}$$

Omil

$$\frac{5 ^ {7}}{2 ^ {4} \cdot 3 \cdot 13} = 125\frac{125}{624} = 125,20032051282051$$