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

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

Avaliar

$$-\frac{625}{18895678704}\approx -0,000000033$$

Passos Para a Resolução

Calcule 3 elevado a 2 e obtenha 9.

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

Multiplique 9 e 2 para obter 18.

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

Calcule 18 elevado a -4 e obtenha \frac{1}{104976}.

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

Calcule 3 elevado a 4 e obtenha 81.

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

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

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

Multiplique 2 e 3 para obter 6.

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

Calcule 6 elevado a 3 e obtenha 216.

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

Calcule 2 elevado a 2 e obtenha 4.

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

Multiplique 216 e 4 para obter 864.

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

Calcule 3 elevado a 3 e obtenha 27.

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

Multiplique 864 e 27 para obter 23328.

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

Calcule 2 elevado a 3 e obtenha 8.

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

Subtraia 3 de 8 para obter 5.

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

Calcule 5 elevado a -4 e obtenha \frac{1}{625}.

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

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

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

Divida -\frac{1}{1296} por \frac{14579999}{625} ao multiplicar -\frac{1}{1296} pelo recíproco de \frac{14579999}{625}.

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

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

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

Fatorizar

$$-\frac{625}{18895678704} = -3,307634564445122 \times 10^{-8}$$