Resolver 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}}

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

Avaliar

$$79716150$$

Passos Para a Resolução

Calcule 27 elevado a 12 e obtenha 150094635296999121.

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

Calcule 243 elevado a 4 e obtenha 3486784401.

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

Multiplique 150094635296999121 e 3486784401 para obter 523347633027360537213511521.

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

Calcule \sqrt[4]{523347633027360537213511521} e obtenha 4782969.

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

Calcule -10 elevado a 2 e obtenha 100.

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

Calcule a raiz quadrada de 100 e obtenha 10.

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

Calcule 5 elevado a 40 e obtenha 9094947017729282379150390625.

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

Calcule a raiz quadrada de 9094947017729282379150390625 e obtenha 95367431640625.

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

Calcule \sqrt[5]{95367431640625} e obtenha 625.

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

Calcule 2 elevado a 18 e obtenha 262144.

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

Calcule \sqrt[3]{262144} e obtenha 64.

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

Calcule a raiz quadrada de 64 e obtenha 8.

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

Multiplique 625 e 8 para obter 5000.

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

Multiplique 16 e 81 para obter 1296.

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

Multiplique 1296 e 625 para obter 810000.

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

Calcule \sqrt[4]{810000} e obtenha 30.

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

Reduza a fração \frac{5000}{30} para os termos mais baixos ao retirar e anular 10.

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

Multiplique \frac{4782969}{10} e \frac{500}{3} para obter 79716150.

$$79716150$$

Fatorizar

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