Solve {[8^{2}:(2^{2}:2*3^{2}-2^{1}-2^{3})-(5*2^2):5]*(2^5:2^4)+2*3^3}:31

$$\{ [ 8 ^ { 2 } : ( 2 ^ { 2 } : 2 \cdot 3 ^ { 2 } - 2 ^ { 1 } - 2 ^ { 3 } ) - ( 5 \cdot 2 ^ { 2 } ) : 5 ] \cdot ( 2 ^ { 5 } : 2 ^ { 4 } ) + 2 \cdot 3 ^ { 3 } \} : 31$$

Evaluate

$$2$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 2 to get 1.

$$\frac{\left(\frac{8^{2}}{2^{1}\times 3^{2}-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times \frac{2^{5}}{2^{4}}+2\times 3^{3}}{31}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{\left(\frac{8^{2}}{2^{1}\times 3^{2}-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{\left(\frac{64}{2^{1}\times 3^{2}-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{\left(\frac{64}{2\times 3^{2}-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(\frac{64}{2\times 9-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Multiply 2 and 9 to get 18.

$$\frac{\left(\frac{64}{18-2^{1}-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{\left(\frac{64}{18-2-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Subtract 2 from 18 to get 16.

$$\frac{\left(\frac{64}{16-2^{3}}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(\frac{64}{16-8}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Subtract 8 from 16 to get 8.

$$\frac{\left(\frac{64}{8}-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Divide 64 by 8 to get 8.

$$\frac{\left(8-\frac{5\times 2^{2}}{5}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Cancel out 5 and 5.

$$\frac{\left(8-2^{2}\right)\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\left(8-4\right)\times 2^{1}+2\times 3^{3}}{31}$$

Subtract 4 from 8 to get 4.

$$\frac{4\times 2^{1}+2\times 3^{3}}{31}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{4\times 2+2\times 3^{3}}{31}$$

Multiply 4 and 2 to get 8.

$$\frac{8+2\times 3^{3}}{31}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{8+2\times 27}{31}$$

Multiply 2 and 27 to get 54.

$$\frac{8+54}{31}$$

Add 8 and 54 to get 62.

$$\frac{62}{31}$$

Divide 62 by 31 to get 2.

$$2$$

Factor

$$2$$