Solve (-4^{2}+8)+2[-3^2div(-1)^2+4(-2)]+[-2^4+(-2)^4]

$$( - 4 ^ { 2 } + 8 ) + 2 [ - 3 ^ { 2 } \div ( - 1 ) ^ { 2 } + 4 ( - 2 ) ] + [ - 2 ^ { 4 } + ( - 2 ) ^ { 4 } ]$$

Evaluate

$$-42$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$-16+8+2\left(\frac{-3^{2}}{\left(-1\right)^{2}}+4\left(-2\right)\right)-2^{4}+\left(-2\right)^{4}$$

Add -16 and 8 to get -8.

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

Calculate 3 to the power of 2 and get 9.

$$-8+2\left(\frac{-9}{\left(-1\right)^{2}}+4\left(-2\right)\right)-2^{4}+\left(-2\right)^{4}$$

Calculate -1 to the power of 2 and get 1.

$$-8+2\left(\frac{-9}{1}+4\left(-2\right)\right)-2^{4}+\left(-2\right)^{4}$$

Anything divided by one gives itself.

$$-8+2\left(-9+4\left(-2\right)\right)-2^{4}+\left(-2\right)^{4}$$

Multiply 4 and -2 to get -8.

$$-8+2\left(-9-8\right)-2^{4}+\left(-2\right)^{4}$$

Subtract 8 from -9 to get -17.

$$-8+2\left(-17\right)-2^{4}+\left(-2\right)^{4}$$

Multiply 2 and -17 to get -34.

$$-8-34-2^{4}+\left(-2\right)^{4}$$

Subtract 34 from -8 to get -42.

$$-42-2^{4}+\left(-2\right)^{4}$$

Calculate 2 to the power of 4 and get 16.

$$-42-16+\left(-2\right)^{4}$$

Subtract 16 from -42 to get -58.

$$-58+\left(-2\right)^{4}$$

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

$$-58+16$$

Add -58 and 16 to get -42.

$$-42$$

Factor

$$-42$$