Solve {[5^{3}-(5^{2}-6^{2}:2)^2:7-3]:(5*2^2+3)-1}^3:2^4

$$\{ [ 5 ^ { 3 } - ( 5 ^ { 2 } - 6 ^ { 2 } : 2 ) ^ { 2 } : 7 - 3 ] : ( 5 \cdot 2 ^ { 2 } + 3 ) - 1 \} ^ { 3 } : 2 ^ { 4 }$$

Evaluate

$$4$$

Solution Steps

Calculate 5 to the power of 3 and get 125.

$$\frac{\left(\frac{125-\frac{\left(5^{2}-\frac{6^{2}}{2}\right)^{2}}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{\left(\frac{125-\frac{\left(25-\frac{6^{2}}{2}\right)^{2}}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{\left(\frac{125-\frac{\left(25-\frac{36}{2}\right)^{2}}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Divide 36 by 2 to get 18.

$$\frac{\left(\frac{125-\frac{\left(25-18\right)^{2}}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Subtract 18 from 25 to get 7.

$$\frac{\left(\frac{125-\frac{7^{2}}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Calculate 7 to the power of 2 and get 49.

$$\frac{\left(\frac{125-\frac{49}{7}-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Divide 49 by 7 to get 7.

$$\frac{\left(\frac{125-7-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Subtract 7 from 125 to get 118.

$$\frac{\left(\frac{118-3}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Subtract 3 from 118 to get 115.

$$\frac{\left(\frac{115}{5\times 2^{2}+3}-1\right)^{3}}{2^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(\frac{115}{5\times 4+3}-1\right)^{3}}{2^{4}}$$

Multiply 5 and 4 to get 20.

$$\frac{\left(\frac{115}{20+3}-1\right)^{3}}{2^{4}}$$

Add 20 and 3 to get 23.

$$\frac{\left(\frac{115}{23}-1\right)^{3}}{2^{4}}$$

Divide 115 by 23 to get 5.

$$\frac{\left(5-1\right)^{3}}{2^{4}}$$

Subtract 1 from 5 to get 4.

$$\frac{4^{3}}{2^{4}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{64}{16}$$

Divide 64 by 16 to get 4.

$$4$$

Factor

$$2^{2}$$