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

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

Evaluate

$$3$$

Solution Steps

Calculate 7 to the power of 2 and get 49.

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

Calculate 2 to the power of 3 and get 8.

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

Multiply 5 and 8 to get 40.

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

Add 49 and 40 to get 89.

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

Calculate 5 to the power of 2 and get 25.

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

Subtract 25 from 89 to get 64.

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

Calculate 2 to the power of 4 and get 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 by 16 to get 4.

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

Calculate 4 to the power of 2 and get 16.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 4 and 3 to get 12.

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

Subtract 12 from 16 to get 4.

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

Calculate 4 to the power of 4 and get 256.

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

Calculate 4 to the power of 2 and get 16.

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

Divide 256 by 16 to get 16.

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

Add 4 and 16 to get 20.

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

Calculate 2 to the power of 2 and get 4.

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

Multiply 3 and 4 to get 12.

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

Subtract 12 from 20 to get 8.

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

Calculate 2 to the power of 3 and get 8.

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

Divide 8 by 8 to get 1.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$