Lutasin ang 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}}

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

I-evaluate

$$79716150$$

Mga Hakbang ng Solution

Kalkulahin ang 27 sa power ng 12 at kunin ang 150094635296999121.

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

Kalkulahin ang 243 sa power ng 4 at kunin ang 3486784401.

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

I-multiply ang 150094635296999121 at 3486784401 para makuha ang 523347633027360537213511521.

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

Kalkulahin ang \sqrt[4]{523347633027360537213511521} at makuha ang 4782969.

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

Kalkulahin ang -10 sa power ng 2 at kunin ang 100.

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

Kalkulahin ang square root ng 100 at makuha ang 10.

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

Kalkulahin ang 5 sa power ng 40 at kunin ang 9094947017729282379150390625.

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

Kalkulahin ang square root ng 9094947017729282379150390625 at makuha ang 95367431640625.

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

Kalkulahin ang \sqrt[5]{95367431640625} at makuha ang 625.

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

Kalkulahin ang 2 sa power ng 18 at kunin ang 262144.

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

Kalkulahin ang \sqrt[3]{262144} at makuha ang 64.

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

Kalkulahin ang square root ng 64 at makuha ang 8.

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

I-multiply ang 625 at 8 para makuha ang 5000.

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

I-multiply ang 16 at 81 para makuha ang 1296.

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

I-multiply ang 1296 at 625 para makuha ang 810000.

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

Kalkulahin ang \sqrt[4]{810000} at makuha ang 30.

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

Bawasan ang fraction \frac{5000}{30} sa pinakamabababang term sa pamamagitan ng pag-extract at pag-cancel out sa 10.

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

I-multiply ang \frac{4782969}{10} at \frac{500}{3} para makuha ang 79716150.

$$79716150$$

I-factor

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