Resolver frac{-(3^{2}*2)^{-4}*3^{4}}{(2*3)^{3}*2^2*3^3-(2^3-3)^-4}

$$\frac { - ( 3 ^ { 2 } \cdot 2 ) ^ { - 4 } \cdot 3 ^ { 4 } } { ( 2 \cdot 3 ) ^ { 3 } \cdot 2 ^ { 2 } \cdot 3 ^ { 3 } - ( 2 ^ { 3 } - 3 ) ^ { - 4 } }$$

Calcular

$$-\frac{625}{18895678704}\approx -0.000000033$$

Pasos da solución

Calcula 3 á potencia de 2 e obtén 9.

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

Multiplica 9 e 2 para obter 18.

$$\frac{\left(-18^{-4}\right)\times 3^{4}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calcula 18 á potencia de -4 e obtén \frac{1}{104976}.

$$\frac{-\frac{1}{104976}\times 3^{4}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calcula 3 á potencia de 4 e obtén 81.

$$\frac{-\frac{1}{104976}\times 81}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiplica -\frac{1}{104976} e 81 para obter -\frac{1}{1296}.

$$\frac{-\frac{1}{1296}}{\left(2\times 3\right)^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiplica 2 e 3 para obter 6.

$$\frac{-\frac{1}{1296}}{6^{3}\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calcula 6 á potencia de 3 e obtén 216.

$$\frac{-\frac{1}{1296}}{216\times 2^{2}\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{-\frac{1}{1296}}{216\times 4\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Multiplica 216 e 4 para obter 864.

$$\frac{-\frac{1}{1296}}{864\times 3^{3}-\left(2^{3}-3\right)^{-4}}$$

Calcula 3 á potencia de 3 e obtén 27.

$$\frac{-\frac{1}{1296}}{864\times 27-\left(2^{3}-3\right)^{-4}}$$

Multiplica 864 e 27 para obter 23328.

$$\frac{-\frac{1}{1296}}{23328-\left(2^{3}-3\right)^{-4}}$$

Calcula 2 á potencia de 3 e obtén 8.

$$\frac{-\frac{1}{1296}}{23328-\left(8-3\right)^{-4}}$$

Resta 3 de 8 para obter 5.

$$\frac{-\frac{1}{1296}}{23328-5^{-4}}$$

Calcula 5 á potencia de -4 e obtén \frac{1}{625}.

$$\frac{-\frac{1}{1296}}{23328-\frac{1}{625}}$$

Resta \frac{1}{625} de 23328 para obter \frac{14579999}{625}.

$$\frac{-\frac{1}{1296}}{\frac{14579999}{625}}$$

Divide -\frac{1}{1296} entre \frac{14579999}{625} mediante a multiplicación de -\frac{1}{1296} polo recíproco de \frac{14579999}{625}.

$$-\frac{1}{1296}\times \frac{625}{14579999}$$

Multiplica -\frac{1}{1296} e \frac{625}{14579999} para obter -\frac{625}{18895678704}.

$$-\frac{625}{18895678704}$$

Factorizar

$$-\frac{625}{18895678704} = -3.307634564445122 \times 10^{-8}$$