Solve {[(-2)^{5}:2^{2}-(-3)^{4}:3^2]:(3-20)-2^6:(-2)^4}*3^2

$$\{ [ ( - 2 ) ^ { 5 } : 2 ^ { 2 } - ( - 3 ) ^ { 4 } : 3 ^ { 2 } ] : ( 3 - 20 ) - 2 ^ { 6 } : ( - 2 ) ^ { 4 } \} \cdot 3 ^ { 2 }$$

Evaluate

$$-27$$

Solution Steps

Calculate -2 to the power of 5 and get -32.

$$\left(\frac{\frac{-32}{2^{2}}-\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\left(\frac{\frac{-32}{4}-\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Divide -32 by 4 to get -8.

$$\left(\frac{-8-\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Calculate -3 to the power of 4 and get 81.

$$\left(\frac{-8-\frac{81}{3^{2}}}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{-8-\frac{81}{9}}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Divide 81 by 9 to get 9.

$$\left(\frac{-8-9}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Subtract 9 from -8 to get -17.

$$\left(\frac{-17}{3-20}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Subtract 20 from 3 to get -17.

$$\left(\frac{-17}{-17}-\frac{2^{6}}{\left(-2\right)^{4}}\right)\times 3^{2}$$

Divide -17 by -17 to get 1.

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

Calculate 2 to the power of 6 and get 64.

$$\left(1-\frac{64}{\left(-2\right)^{4}}\right)\times 3^{2}$$

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

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

Divide 64 by 16 to get 4.

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

Subtract 4 from 1 to get -3.

$$-3\times 3^{2}$$

Calculate 3 to the power of 2 and get 9.

$$-3\times 9$$

Multiply -3 and 9 to get -27.

$$-27$$

Factor

$$-27$$