Resolver 16^{-frac{2/2}27^{-1}81^frac{1{4}}}{16^-227^-frac{4{2}}81^frac{2{4}}}

$$\frac { 16 ^ { - \frac { 2 } { 2 } } 27 ^ { - 1 } 81 ^ { \frac { 1 } { 4 } } } { 16 ^ { - 2 } 27 ^ { - \frac { 4 } { 2 } } 81 ^ { \frac { 2 } { 4 } } }$$

Calcular

$$144$$

Pasos da solución

Divide 2 entre 2 para obter 1.

$$\frac{16^{-1}\times 27^{-1}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Calcula 16 á potencia de -1 e obtén \frac{1}{16}.

$$\frac{\frac{1}{16}\times 27^{-1}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

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

$$\frac{\frac{1}{16}\times \frac{1}{27}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Multiplica \frac{1}{16} e \frac{1}{27} para obter \frac{1}{432}.

$$\frac{\frac{1}{432}\times 81^{\frac{1}{4}}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Calcula 81 á potencia de \frac{1}{4} e obtén 3.

$$\frac{\frac{1}{432}\times 3}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Multiplica \frac{1}{432} e 3 para obter \frac{1}{144}.

$$\frac{\frac{1}{144}}{16^{-2}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Calcula 16 á potencia de -2 e obtén \frac{1}{256}.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times 27^{-\frac{4}{2}}\times 81^{\frac{2}{4}}}$$

Divide 4 entre 2 para obter 2.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times 27^{-2}\times 81^{\frac{2}{4}}}$$

Calcula 27 á potencia de -2 e obtén \frac{1}{729}.

$$\frac{\frac{1}{144}}{\frac{1}{256}\times \frac{1}{729}\times 81^{\frac{2}{4}}}$$

Multiplica \frac{1}{256} e \frac{1}{729} para obter \frac{1}{186624}.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 81^{\frac{2}{4}}}$$

Reduce a fracción \frac{2}{4} a termos máis baixos extraendo e cancelando 2.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 81^{\frac{1}{2}}}$$

Calcula 81 á potencia de \frac{1}{2} e obtén 9.

$$\frac{\frac{1}{144}}{\frac{1}{186624}\times 9}$$

Multiplica \frac{1}{186624} e 9 para obter \frac{1}{20736}.

$$\frac{\frac{1}{144}}{\frac{1}{20736}}$$

Divide \frac{1}{144} entre \frac{1}{20736} mediante a multiplicación de \frac{1}{144} polo recíproco de \frac{1}{20736}.

$$\frac{1}{144}\times 20736$$

Multiplica \frac{1}{144} e 20736 para obter 144.

$$144$$

Factorizar

$$2^{4}\times 3^{2}$$