frac{(4^{2})^{3}*6^{3}*6^{2}*(6^{2})^{3}*4^{0}*4^{-2}}{(6^{3})^2-4^-2*4^5*6^3} eching

$$\frac { ( 4 ^ { 2 } ) ^ { 3 } \cdot 6 ^ { 3 } \cdot 6 ^ { 2 } \cdot ( 6 ^ { 2 } ) ^ { 3 } \cdot 4 ^ { 0 } \cdot 4 ^ { - 2 } } { ( 6 ^ { 3 } ) ^ { 2 } - 4 ^ { - 2 } \cdot 4 ^ { 5 } \cdot 6 ^ { 3 } }$$

Baholash

$$\frac{53747712}{19}\approx 2828826,947368421$$

Yechim qadamlari

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

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times \left(6^{2}\right)^{3}\times 4^{0}\times 4^{-2}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

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

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times 6^{6}\times 4^{0}\times 4^{-2}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 6 va 0 ni qo‘shib, 6 ni oling.

$$\frac{4^{6}\times 6^{3}\times 6^{2}\times 6^{6}\times 4^{-2}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

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

$$\frac{4^{4}\times 6^{3}\times 6^{2}\times 6^{6}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

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

$$\frac{4^{4}\times 6^{5}\times 6^{6}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 5 va 6 ni qo‘shib, 11 ni oling.

$$\frac{4^{4}\times 6^{11}}{\left(6^{3}\right)^{2}-4^{-2}\times 4^{5}\times 6^{3}}$$

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

$$\frac{4^{4}\times 6^{11}}{6^{6}-4^{-2}\times 4^{5}\times 6^{3}}$$

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

$$\frac{4^{4}\times 6^{11}}{6^{6}-4^{3}\times 6^{3}}$$

4 daraja ko‘rsatkichini 4 ga hisoblang va 256 ni qiymatni oling.

$$\frac{256\times 6^{11}}{6^{6}-4^{3}\times 6^{3}}$$

11 daraja ko‘rsatkichini 6 ga hisoblang va 362797056 ni qiymatni oling.

$$\frac{256\times 362797056}{6^{6}-4^{3}\times 6^{3}}$$

92876046336 hosil qilish uchun 256 va 362797056 ni ko'paytirish.

$$\frac{92876046336}{6^{6}-4^{3}\times 6^{3}}$$

6 daraja ko‘rsatkichini 6 ga hisoblang va 46656 ni qiymatni oling.

$$\frac{92876046336}{46656-4^{3}\times 6^{3}}$$

3 daraja ko‘rsatkichini 4 ga hisoblang va 64 ni qiymatni oling.

$$\frac{92876046336}{46656-64\times 6^{3}}$$

3 daraja ko‘rsatkichini 6 ga hisoblang va 216 ni qiymatni oling.

$$\frac{92876046336}{46656-64\times 216}$$

13824 hosil qilish uchun 64 va 216 ni ko'paytirish.

$$\frac{92876046336}{46656-13824}$$

32832 olish uchun 46656 dan 13824 ni ayirish.

$$\frac{92876046336}{32832}$$

\frac{92876046336}{32832} ulushini 1728 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{53747712}{19}$$

Omil

$$\frac{2 ^ {13} \cdot 3 ^ {8}}{19} = 2828826\frac{18}{19} = 2828826,947368421$$