Resolver {[(7^{2}+5*2^{3}-5^{2}):2^{4}+(4^{2}-2^{2}*3)^4:4^2-3*2^2]:2^3}+2

$$\{ [ ( 7 ^ { 2 } + 5 \times 2 ^ { 3 } - 5 ^ { 2 } ) : 2 ^ { 4 } + ( 4 ^ { 2 } - 2 ^ { 2 } \times 3 ) ^ { 4 } : 4 ^ { 2 } - 3 \times 2 ^ { 2 } ] : 2 ^ { 3 } \} + 2$$

Calcular

$$3$$

Pasos da solución

Calcula 7 á potencia de 2 e obtén 49.

$$\frac{\frac{49+5\times 2^{3}-5^{2}}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 2 á potencia de 3 e obtén 8.

$$\frac{\frac{49+5\times 8-5^{2}}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Multiplica 5 e 8 para obter 40.

$$\frac{\frac{49+40-5^{2}}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Suma 49 e 40 para obter 89.

$$\frac{\frac{89-5^{2}}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 5 á potencia de 2 e obtén 25.

$$\frac{\frac{89-25}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Resta 25 de 89 para obter 64.

$$\frac{\frac{64}{2^{4}}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 2 á potencia de 4 e obtén 16.

$$\frac{\frac{64}{16}+\frac{\left(4^{2}-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Divide 64 entre 16 para obter 4.

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

Calcula 4 á potencia de 2 e obtén 16.

$$\frac{4+\frac{\left(16-2^{2}\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{4+\frac{\left(16-4\times 3\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Multiplica 4 e 3 para obter 12.

$$\frac{4+\frac{\left(16-12\right)^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Resta 12 de 16 para obter 4.

$$\frac{4+\frac{4^{4}}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 4 á potencia de 4 e obtén 256.

$$\frac{4+\frac{256}{4^{2}}-3\times 2^{2}}{2^{3}}+2$$

Calcula 4 á potencia de 2 e obtén 16.

$$\frac{4+\frac{256}{16}-3\times 2^{2}}{2^{3}}+2$$

Divide 256 entre 16 para obter 16.

$$\frac{4+16-3\times 2^{2}}{2^{3}}+2$$

Suma 4 e 16 para obter 20.

$$\frac{20-3\times 2^{2}}{2^{3}}+2$$

Calcula 2 á potencia de 2 e obtén 4.

$$\frac{20-3\times 4}{2^{3}}+2$$

Multiplica 3 e 4 para obter 12.

$$\frac{20-12}{2^{3}}+2$$

Resta 12 de 20 para obter 8.

$$\frac{8}{2^{3}}+2$$

Calcula 2 á potencia de 3 e obtén 8.

$$\frac{8}{8}+2$$

Divide 8 entre 8 para obter 1.

$$1+2$$

Suma 1 e 2 para obter 3.

$$3$$

Factorizar

$$3$$