Resolver {5^{3}*3^{2}-2^{3}*[(6^{2}+6^{2}*15):2^{3}+3^2*17-6*(2^2*14-12^2:3^2*2)]}:53

$$\{ 5 ^ { 3 } \cdot 3 ^ { 2 } - 2 ^ { 3 } \cdot [ ( 6 ^ { 2 } + 6 ^ { 2 } \cdot 15 ) : 2 ^ { 3 } + 3 ^ { 2 } \cdot 17 - 6 \cdot ( 2 ^ { 2 } \cdot 14 - 12 ^ { 2 } : 3 ^ { 2 } \cdot 2 ) ] \} : 53$$

Calcular

$$9$$

Pasos da solución

Calcula 5 á potencia de 3 e obtén 125.

$$\frac{125\times 3^{2}-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 3 á potencia de 2 e obtén 9.

$$\frac{125\times 9-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiplica 125 e 9 para obter 1125.

$$\frac{1125-2^{3}\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 2 á potencia de 3 e obtén 8.

$$\frac{1125-8\left(\frac{6^{2}+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 6 á potencia de 2 e obtén 36.

$$\frac{1125-8\left(\frac{36+6^{2}\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 6 á potencia de 2 e obtén 36.

$$\frac{1125-8\left(\frac{36+36\times 15}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiplica 36 e 15 para obter 540.

$$\frac{1125-8\left(\frac{36+540}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Suma 36 e 540 para obter 576.

$$\frac{1125-8\left(\frac{576}{2^{3}}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 2 á potencia de 3 e obtén 8.

$$\frac{1125-8\left(\frac{576}{8}+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Divide 576 entre 8 para obter 72.

$$\frac{1125-8\left(72+3^{2}\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 3 á potencia de 2 e obtén 9.

$$\frac{1125-8\left(72+9\times 17-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiplica 9 e 17 para obter 153.

$$\frac{1125-8\left(72+153-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Suma 72 e 153 para obter 225.

$$\frac{1125-8\left(225-6\left(2^{2}\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{1125-8\left(225-6\left(4\times 14-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Multiplica 4 e 14 para obter 56.

$$\frac{1125-8\left(225-6\left(56-\frac{12^{2}}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 12 á potencia de 2 e obtén 144.

$$\frac{1125-8\left(225-6\left(56-\frac{144}{3^{2}}\times 2\right)\right)}{53}$$

Calcula 3 á potencia de 2 e obtén 9.

$$\frac{1125-8\left(225-6\left(56-\frac{144}{9}\times 2\right)\right)}{53}$$

Divide 144 entre 9 para obter 16.

$$\frac{1125-8\left(225-6\left(56-16\times 2\right)\right)}{53}$$

Multiplica 16 e 2 para obter 32.

$$\frac{1125-8\left(225-6\left(56-32\right)\right)}{53}$$

Resta 32 de 56 para obter 24.

$$\frac{1125-8\left(225-6\times 24\right)}{53}$$

Multiplica 6 e 24 para obter 144.

$$\frac{1125-8\left(225-144\right)}{53}$$

Resta 144 de 225 para obter 81.

$$\frac{1125-8\times 81}{53}$$

Multiplica 8 e 81 para obter 648.

$$\frac{1125-648}{53}$$

Resta 648 de 1125 para obter 477.

$$\frac{477}{53}$$

Divide 477 entre 53 para obter 9.

$$9$$

Factorizar

$$3^{2}$$