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

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

Evaluate

$$-33$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

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

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

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

Calculate the square root of 16 and get 4.

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

Multiply -8 and 4 to get -32.

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

Calculate -4 to the power of 3 and get -64.

$$-32+\sqrt[3]{-64}\left(-\frac{1}{2}\right)^{2}$$

Calculate \sqrt[3]{-64} and get -4.

$$-32-4\left(-\frac{1}{2}\right)^{2}$$

Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.

$$-32-4\times \frac{1}{4}$$

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

$$-32-1$$

Subtract 1 from -32 to get -33.

$$-33$$

Factor

$$-33$$