Solve (-2)^{4}-(2^{2})^{3}*(3-5)^2+(-4)^2div(-2^2)-(-1^4)

$$( - 2 ) ^ { 4 } - ( 2 ^ { 2 } ) ^ { 3 } \times ( 3 - 5 ) ^ { 2 } + ( - 4 ) ^ { 2 } \div ( - 2 ^ { 2 } ) - ( - 1 ^ { 4 } )$$

Evaluate

$$-243$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

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

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

$$16-2^{6}\left(3-5\right)^{2}+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

Calculate 2 to the power of 6 and get 64.

$$16-64\left(3-5\right)^{2}+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

Subtract 5 from 3 to get -2.

$$16-64\left(-2\right)^{2}+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

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

$$16-64\times 4+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

Multiply 64 and 4 to get 256.

$$16-256+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

Subtract 256 from 16 to get -240.

$$-240+\frac{\left(-4\right)^{2}}{-2^{2}}-\left(-1^{4}\right)$$

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

$$-240+\frac{16}{-2^{2}}-\left(-1^{4}\right)$$

Calculate 2 to the power of 2 and get 4.

$$-240+\frac{16}{-4}-\left(-1^{4}\right)$$

Divide 16 by -4 to get -4.

$$-240-4-\left(-1^{4}\right)$$

Subtract 4 from -240 to get -244.

$$-244-\left(-1^{4}\right)$$

Calculate 1 to the power of 4 and get 1.

$$-244-\left(-1\right)$$

The opposite of -1 is 1.

$$-244+1$$

Add -244 and 1 to get -243.

$$-243$$

Factor

$$-243$$