frac{sqrt[4]{27^{12}*243^4}}{sqrt{(-10)^2}}*frac{sqrt[5]{sqrt{5^40}}*sqrt{sqrt[3]{2^18}}}{sqrt[4]{16*81*625}} eching

$$\frac { \sqrt[ 4 ] { 27 ^ { 12 } \cdot 243 ^ { 4 } } } { \sqrt { ( - 10 ) ^ { 2 } } } \times \frac { \sqrt[ 5 ] { \sqrt { 5 ^ { 40 } } } \cdot \sqrt { \sqrt[ 3 ] { 2 ^ { 18 } } } } { \sqrt[ 4 ] { 16 \cdot 81 \cdot 625 } }$$

Baholash

$$79716150$$

Yechim qadamlari

12 daraja ko‘rsatkichini 27 ga hisoblang va 150094635296999121 ni qiymatni oling.

$$\frac{\sqrt[4]{150094635296999121\times 243^{4}}}{\sqrt{\left(-10\right)^{2}}}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

4 daraja ko‘rsatkichini 243 ga hisoblang va 3486784401 ni qiymatni oling.

$$\frac{\sqrt[4]{150094635296999121\times 3486784401}}{\sqrt{\left(-10\right)^{2}}}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

523347633027360537213511521 hosil qilish uchun 150094635296999121 va 3486784401 ni ko'paytirish.

$$\frac{\sqrt[4]{523347633027360537213511521}}{\sqrt{\left(-10\right)^{2}}}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

\sqrt[4]{523347633027360537213511521} ni hisoblab, 4782969 natijasiga ega bo‘ling.

$$\frac{4782969}{\sqrt{\left(-10\right)^{2}}}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

2 daraja ko‘rsatkichini -10 ga hisoblang va 100 ni qiymatni oling.

$$\frac{4782969}{\sqrt{100}}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

100 ning kvadrat ildizini hisoblab, 10 natijaga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{\sqrt[5]{\sqrt{5^{40}}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

40 daraja ko‘rsatkichini 5 ga hisoblang va 9094947017729282379150390625 ni qiymatni oling.

$$\frac{4782969}{10}\times \frac{\sqrt[5]{\sqrt{9094947017729282379150390625}}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

9094947017729282379150390625 ning kvadrat ildizini hisoblab, 95367431640625 natijaga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{\sqrt[5]{95367431640625}\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

\sqrt[5]{95367431640625} ni hisoblab, 625 natijasiga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{625\sqrt{\sqrt[3]{2^{18}}}}{\sqrt[4]{16\times 81\times 625}}$$

18 daraja ko‘rsatkichini 2 ga hisoblang va 262144 ni qiymatni oling.

$$\frac{4782969}{10}\times \frac{625\sqrt{\sqrt[3]{262144}}}{\sqrt[4]{16\times 81\times 625}}$$

\sqrt[3]{262144} ni hisoblab, 64 natijasiga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{625\sqrt{64}}{\sqrt[4]{16\times 81\times 625}}$$

64 ning kvadrat ildizini hisoblab, 8 natijaga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{625\times 8}{\sqrt[4]{16\times 81\times 625}}$$

5000 hosil qilish uchun 625 va 8 ni ko'paytirish.

$$\frac{4782969}{10}\times \frac{5000}{\sqrt[4]{16\times 81\times 625}}$$

1296 hosil qilish uchun 16 va 81 ni ko'paytirish.

$$\frac{4782969}{10}\times \frac{5000}{\sqrt[4]{1296\times 625}}$$

810000 hosil qilish uchun 1296 va 625 ni ko'paytirish.

$$\frac{4782969}{10}\times \frac{5000}{\sqrt[4]{810000}}$$

\sqrt[4]{810000} ni hisoblab, 30 natijasiga ega bo‘ling.

$$\frac{4782969}{10}\times \frac{5000}{30}$$

\frac{5000}{30} ulushini 10 ni chiqarib, bekor qilish hisobiga eng past shartlarga kamaytiring.

$$\frac{4782969}{10}\times \frac{500}{3}$$

79716150 hosil qilish uchun \frac{4782969}{10} va \frac{500}{3} ni ko'paytirish.

$$79716150$$

Omil

$$2\times 3^{13}\times 5^{2}$$