Solve 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}}

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

Evaluate

$$79716150$$

Solution Steps

Calculate 27 to the power of 12 and get 150094635296999121.

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

Calculate 243 to the power of 4 and get 3486784401.

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

Multiply 150094635296999121 and 3486784401 to get 523347633027360537213511521.

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

Calculate \sqrt[4]{523347633027360537213511521} and get 4782969.

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

Calculate -10 to the power of 2 and get 100.

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

Calculate the square root of 100 and get 10.

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

Calculate 5 to the power of 40 and get 9094947017729282379150390625.

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

Calculate the square root of 9094947017729282379150390625 and get 95367431640625.

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

Calculate \sqrt[5]{95367431640625} and get 625.

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

Calculate 2 to the power of 18 and get 262144.

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

Calculate \sqrt[3]{262144} and get 64.

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

Calculate the square root of 64 and get 8.

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

Multiply 625 and 8 to get 5000.

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

Multiply 16 and 81 to get 1296.

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

Multiply 1296 and 625 to get 810000.

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

Calculate \sqrt[4]{810000} and get 30.

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

Reduce the fraction \frac{5000}{30} to lowest terms by extracting and canceling out 10.

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

Multiply \frac{4782969}{10} and \frac{500}{3} to get 79716150.

$$79716150$$

Factor

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