Solve [(-2)^{6}:2^{3}+(-3)^4:3^2]:(3-20)-2^7:(-2)^4}:3

$$[ ( - 2 ) ^ { 6 } : 2 ^ { 3 } + ( - 3 ) ^ { 4 } : 3 ^ { 2 } ] : ( 3 - 20 ) - 2 ^ { 7 } : ( - 2 ) ^ { 4 } \} : 3$$

Evaluate

$$-9$$

Solution Steps

Calculate -2 to the power of 6 and get 64.

$$\frac{\frac{64}{2^{3}}+\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{64}{8}+\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Divide 64 by 8 to get 8.

$$\frac{8+\frac{\left(-3\right)^{4}}{3^{2}}}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

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

$$\frac{8+\frac{81}{3^{2}}}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{8+\frac{81}{9}}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Divide 81 by 9 to get 9.

$$\frac{8+9}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Add 8 and 9 to get 17.

$$\frac{17}{3-20}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Subtract 20 from 3 to get -17.

$$\frac{17}{-17}-\frac{2^{7}}{\left(-2\right)^{4}}$$

Divide 17 by -17 to get -1.

$$-1-\frac{2^{7}}{\left(-2\right)^{4}}$$

Calculate 2 to the power of 7 and get 128.

$$-1-\frac{128}{\left(-2\right)^{4}}$$

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

$$-1-\frac{128}{16}$$

Divide 128 by 16 to get 8.

$$-1-8$$

Subtract 8 from -1 to get -9.

$$-9$$

Factor

$$-9$$