(3^{2}*2)^{2}:(3^{2}*2)+[3^{3}*2:(2*7^{2}:7+2^2)]^3:3^3+2^2*2 eching

$$( 3 ^ { 2 } \times 2 ) ^ { 2 } : ( 3 ^ { 2 } \times 2 ) + [ 3 ^ { 3 } \times 2 : ( 2 \times 7 ^ { 2 } : 7 + 2 ^ { 2 } ) ] ^ { 3 } : 3 ^ { 3 } + 2 ^ { 2 } \times 2$$

Baholash

$$27$$

Yechim qadamlari

Ayni asosning daraja ko‘rsatkichini bo‘lish uchun maxrajning darajasini surat darajasidan ayiring. 2 dan 1 ni ayirib, 1 ni oling.

$$\left(3^{2}\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{2}\times 2$$

Ayni asosning daraja ko‘rsatkichlarini ko‘paytirish uchun ularning darajalarini qo‘shing. 2 va 1 ni qo‘shib, 3 ni oling.

$$\left(3^{2}\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

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

$$\left(9\times 2\right)^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

18 hosil qilish uchun 9 va 2 ni ko'paytirish.

$$18^{1}+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

1 daraja ko‘rsatkichini 18 ga hisoblang va 18 ni qiymatni oling.

$$18+\frac{\left(\frac{3^{3}\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$18+\frac{\left(\frac{27\times 2}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

54 hosil qilish uchun 27 va 2 ni ko'paytirish.

$$18+\frac{\left(\frac{54}{\frac{2\times 7^{2}}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

2 daraja ko‘rsatkichini 7 ga hisoblang va 49 ni qiymatni oling.

$$18+\frac{\left(\frac{54}{\frac{2\times 49}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

98 hosil qilish uchun 2 va 49 ni ko'paytirish.

$$18+\frac{\left(\frac{54}{\frac{98}{7}+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

14 ni olish uchun 98 ni 7 ga bo‘ling.

$$18+\frac{\left(\frac{54}{14+2^{2}}\right)^{3}}{3^{3}}+2^{3}$$

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

$$18+\frac{\left(\frac{54}{14+4}\right)^{3}}{3^{3}}+2^{3}$$

18 olish uchun 14 va 4'ni qo'shing.

$$18+\frac{\left(\frac{54}{18}\right)^{3}}{3^{3}}+2^{3}$$

3 ni olish uchun 54 ni 18 ga bo‘ling.

$$18+\frac{3^{3}}{3^{3}}+2^{3}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$18+\frac{27}{3^{3}}+2^{3}$$

3 daraja ko‘rsatkichini 3 ga hisoblang va 27 ni qiymatni oling.

$$18+\frac{27}{27}+2^{3}$$

1 ni olish uchun 27 ni 27 ga bo‘ling.

$$18+1+2^{3}$$

19 olish uchun 18 va 1'ni qo'shing.

$$19+2^{3}$$

3 daraja ko‘rsatkichini 2 ga hisoblang va 8 ni qiymatni oling.

$$19+8$$

27 olish uchun 19 va 8'ni qo'shing.

$$27$$

Omil

$$3^{3}$$