Resolver frac{(2^{4}*3^6)^frac{1{2}}*sqrt[3]{8}*sqrt{81}}{16^frac{3{4}}*27^frac{1{3}}}

$$\frac { ( 2 ^ { 4 } \times 3 ^ { 6 } ) ^ { \frac { 1 } { 2 } } \times \sqrt[ 3 ] { 8 } \times \sqrt { 81 } } { 16 ^ { \frac { 3 } { 4 } } \times 27 ^ { \frac { 1 } { 3 } } }$$

Calcular

$$81$$

Pasos da solución

Calcula 2 á potencia de 4 e obtén 16.

$$\frac{\left(16\times 3^{6}\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calcula 3 á potencia de 6 e obtén 729.

$$\frac{\left(16\times 729\right)^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiplica 16 e 729 para obter 11664.

$$\frac{11664^{\frac{1}{2}}\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calcula 11664 á potencia de \frac{1}{2} e obtén 108.

$$\frac{108\sqrt[3]{8}\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calcular \sqrt[3]{8} e obter 2.

$$\frac{108\times 2\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiplica 108 e 2 para obter 216.

$$\frac{216\sqrt{81}}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calcular a raíz cadrada de 81 e obter 9.

$$\frac{216\times 9}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Multiplica 216 e 9 para obter 1944.

$$\frac{1944}{16^{\frac{3}{4}}\times 27^{\frac{1}{3}}}$$

Calcula 16 á potencia de \frac{3}{4} e obtén 8.

$$\frac{1944}{8\times 27^{\frac{1}{3}}}$$

Calcula 27 á potencia de \frac{1}{3} e obtén 3.

$$\frac{1944}{8\times 3}$$

Multiplica 8 e 3 para obter 24.

$$\frac{1944}{24}$$

Divide 1944 entre 24 para obter 81.

$$81$$

Factorizar

$$3^{4}$$