Issolvi 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}}

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

Evalwa

$$79716150$$

Passi tas-Soluzzjonijiet

Ikkalkula 27 bil-power ta' 12 u tikseb 150094635296999121.

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

Ikkalkula 243 bil-power ta' 4 u tikseb 3486784401.

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

Immultiplika 150094635296999121 u 3486784401 biex tikseb 523347633027360537213511521.

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

Ikkalkola \sqrt[4]{523347633027360537213511521} u ikseb 4782969.

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

Ikkalkula -10 bil-power ta' 2 u tikseb 100.

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

Ikkalkula l-għerq kwadrat ta' 100 u ikseb 10.

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

Ikkalkula 5 bil-power ta' 40 u tikseb 9094947017729282379150390625.

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

Ikkalkula l-għerq kwadrat ta' 9094947017729282379150390625 u ikseb 95367431640625.

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

Ikkalkola \sqrt[5]{95367431640625} u ikseb 625.

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

Ikkalkula 2 bil-power ta' 18 u tikseb 262144.

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

Ikkalkola \sqrt[3]{262144} u ikseb 64.

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

Ikkalkula l-għerq kwadrat ta' 64 u ikseb 8.

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

Immultiplika 625 u 8 biex tikseb 5000.

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

Immultiplika 16 u 81 biex tikseb 1296.

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

Immultiplika 1296 u 625 biex tikseb 810000.

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

Ikkalkola \sqrt[4]{810000} u ikseb 30.

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

Naqqas il-frazzjoni \frac{5000}{30} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 10.

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

Immultiplika \frac{4782969}{10} u \frac{500}{3} biex tikseb 79716150.

$$79716150$$

Fattur

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