Resolver 3^2left(2^-1right)^3{left(frac{1/3right)}^3{left(1/4right)}^-2}{6^-3}

$$\frac{ { 3 }^{ 2 } { \left( { 2 }^{ -1 } \right) }^{ 3 } { \left( \frac{ 1 }{ 3 } \right) }^{ 3 } { \left( \frac{ 1 }{ 4 } \right) }^{ -2 } }{ { 6 }^{ -3 } }$$

Calcular

$$144$$

Pasos da solución

Para elevar unha potencia a outra potencia, multiplica os expoñentes. Multiplica -1 e 3 para obter -3.

$$\frac{3^{2}\times 2^{-3}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calcula 3 á potencia de 2 e obtén 9.

$$\frac{9\times 2^{-3}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calcula 2 á potencia de -3 e obtén \frac{1}{8}.

$$\frac{9\times \frac{1}{8}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Multiplica 9 e \frac{1}{8} para obter \frac{9}{8}.

$$\frac{\frac{9}{8}\times \left(\frac{1}{3}\right)^{3}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

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

$$\frac{\frac{9}{8}\times \frac{1}{27}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Multiplica \frac{9}{8} e \frac{1}{27} para obter \frac{1}{24}.

$$\frac{\frac{1}{24}\times \left(\frac{1}{4}\right)^{-2}}{6^{-3}}$$

Calcula \frac{1}{4} á potencia de -2 e obtén 16.

$$\frac{\frac{1}{24}\times 16}{6^{-3}}$$

Multiplica \frac{1}{24} e 16 para obter \frac{2}{3}.

$$\frac{\frac{2}{3}}{6^{-3}}$$

Calcula 6 á potencia de -3 e obtén \frac{1}{216}.

$$\frac{\frac{2}{3}}{\frac{1}{216}}$$

Divide \frac{2}{3} entre \frac{1}{216} mediante a multiplicación de \frac{2}{3} polo recíproco de \frac{1}{216}.

$$\frac{2}{3}\times 216$$

Multiplica \frac{2}{3} e 216 para obter 144.

$$144$$

Factorizar

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