frac{12^{4}*12^{7}+frac{36^{11}}{3^{11}}}{12^15/12^11+2^11*6^11} eching

$$\frac { 12 ^ { 4 } \cdot 12 ^ { 7 } + \frac { 36 ^ { 11 } } { 3 ^ { 11 } } } { \frac { 12 ^ { 15 } } { 12 ^ { 11 } } + 2 ^ { 11 } \cdot 6 ^ { 11 } }$$

Baholash

$$\frac{71663616}{35831809}\approx 1,999999944$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 4 va 7 ni qo‘shib, 11 ni oling.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{\frac{12^{15}}{12^{11}}+2^{11}\times 6^{11}}$$

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 15 dan 11 ni ayirib, 4 ni oling.

$$\frac{12^{11}+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

11 daraja ko‘rsatkichini 12 ga hisoblang va 743008370688 ni qiymatni oling.

$$\frac{743008370688+\frac{36^{11}}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

11 daraja ko‘rsatkichini 36 ga hisoblang va 131621703842267136 ni qiymatni oling.

$$\frac{743008370688+\frac{131621703842267136}{3^{11}}}{12^{4}+2^{11}\times 6^{11}}$$

11 daraja ko‘rsatkichini 3 ga hisoblang va 177147 ni qiymatni oling.

$$\frac{743008370688+\frac{131621703842267136}{177147}}{12^{4}+2^{11}\times 6^{11}}$$

743008370688 ni olish uchun 131621703842267136 ni 177147 ga bo‘ling.

$$\frac{743008370688+743008370688}{12^{4}+2^{11}\times 6^{11}}$$

1486016741376 olish uchun 743008370688 va 743008370688'ni qo'shing.

$$\frac{1486016741376}{12^{4}+2^{11}\times 6^{11}}$$

4 daraja ko‘rsatkichini 12 ga hisoblang va 20736 ni qiymatni oling.

$$\frac{1486016741376}{20736+2^{11}\times 6^{11}}$$

11 daraja ko‘rsatkichini 2 ga hisoblang va 2048 ni qiymatni oling.

$$\frac{1486016741376}{20736+2048\times 6^{11}}$$

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

$$\frac{1486016741376}{20736+2048\times 362797056}$$

743008370688 hosil qilish uchun 2048 va 362797056 ni ko'paytirish.

$$\frac{1486016741376}{20736+743008370688}$$

743008391424 olish uchun 20736 va 743008370688'ni qo'shing.

$$\frac{1486016741376}{743008391424}$$

\frac{1486016741376}{743008391424} ulushini 20736 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{71663616}{35831809}$$

Omil

$$\frac{2 ^ {15} \cdot 3 ^ {7}}{13 \cdot 211 \cdot 13063} = 1\frac{35831807}{35831809} = 1,9999999441836722$$