Lahenda 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}}

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

Arvuta

$$79716150$$

Lahenduse etapid

Arvutage 12 aste 27 ja leidke 150094635296999121.

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

Arvutage 4 aste 243 ja leidke 3486784401.

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

Korrutage 150094635296999121 ja 3486784401, et leida 523347633027360537213511521.

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

Arvutage \sqrt[4]{523347633027360537213511521}, et saada 4782969.

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

Arvutage 2 aste -10 ja leidke 100.

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

Arvutage 100 ruutjuur, et saada 10.

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

Arvutage 40 aste 5 ja leidke 9094947017729282379150390625.

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

Arvutage 9094947017729282379150390625 ruutjuur, et saada 95367431640625.

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

Arvutage \sqrt[5]{95367431640625}, et saada 625.

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

Arvutage 18 aste 2 ja leidke 262144.

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

Arvutage \sqrt[3]{262144}, et saada 64.

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

Arvutage 64 ruutjuur, et saada 8.

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

Korrutage 625 ja 8, et leida 5000.

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

Korrutage 16 ja 81, et leida 1296.

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

Korrutage 1296 ja 625, et leida 810000.

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

Arvutage \sqrt[4]{810000}, et saada 30.

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

Taandage murd \frac{5000}{30} vähimale ühiskordsele, eraldades ja taandades arvu 10.

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

Korrutage \frac{4782969}{10} ja \frac{500}{3}, et leida 79716150.

$$79716150$$

Lahuta teguriteks

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