(frac{5^{4}*2^7*5^2}{3^2*4^2}) eching

$$( \frac { 5 ^ { 4 } \times 2 ^ { 7 } \times 5 ^ { 2 } } { 3 ^ { 2 } \times 4 ^ { 2 } } )$$

Baholash

$$\frac{125000}{9}\approx 13888,888888889$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 2 ni qo‘shib, 6 ni oling.

$$\frac{5^{6}\times 2^{7}}{3^{2}\times 4^{2}}$$

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

$$\frac{15625\times 2^{7}}{3^{2}\times 4^{2}}$$

7 daraja ko‘rsatkichini 2 ga hisoblang va 128 ni qiymatni oling.

$$\frac{15625\times 128}{3^{2}\times 4^{2}}$$

2000000 hosil qilish uchun 15625 va 128 ni ko'paytirish.

$$\frac{2000000}{3^{2}\times 4^{2}}$$

2 daraja ko‘rsatkichini 3 ga hisoblang va 9 ni qiymatni oling.

$$\frac{2000000}{9\times 4^{2}}$$

2 daraja ko‘rsatkichini 4 ga hisoblang va 16 ni qiymatni oling.

$$\frac{2000000}{9\times 16}$$

144 hosil qilish uchun 9 va 16 ni ko'paytirish.

$$\frac{2000000}{144}$$

\frac{2000000}{144} ulushini 16 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{125000}{9}$$

Omil

$$\frac{2 ^ {3} \cdot 5 ^ {6}}{3 ^ {2}} = 13888\frac{8}{9} = 13888,888888888889$$