Solve sqrt[3]{1/4(-32)}+(sqrt{2^4-(-4)^2})^2

$$\sqrt[ 3 ] { \frac { 1 } { 4 } ( - 32 ) } + ( \sqrt { 2 ^ { 4 } - ( - 4 ) ^ { 2 } } ) ^ { 2 }$$

Evaluate

$$-2$$

Solution Steps

Multiply \frac{1}{4} and -32 to get -8.

$$\sqrt[3]{-8}+\left(\sqrt{2^{4}-\left(-4\right)^{2}}\right)^{2}$$

Calculate \sqrt[3]{-8} and get -2.

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

Calculate 2 to the power of 4 and get 16.

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

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

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

Subtract 16 from 16 to get 0.

$$-2+\left(\sqrt{0}\right)^{2}$$

The square of \sqrt{0} is 0.

$$-2+0$$

Add -2 and 0 to get -2.

$$-2$$

Factor

$$-2$$