Solve (2)(-2)^3*sqrt{(-4)^2}+sqrt[3]{(-4)^3}*(-1/2)^2-sqrt[3]{27}

$$( 2 ) ( - 2 ) ^ { 3 } \times \sqrt { ( - 4 ) ^ { 2 } } + \sqrt[ 3 ] { ( - 4 ) ^ { 3 } } \times ( - \frac { 1 } { 2 } ) ^ { 2 } - \sqrt[ 3 ] { 27 }$$

Evaluate

$$-68$$

Solution Steps

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

$$2\left(-8\right)\sqrt{\left(-4\right)^{2}}+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

Multiply 2 and -8 to get -16.

$$-16\sqrt{\left(-4\right)^{2}}+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-16\sqrt{16}+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

Calculate the square root of 16 and get 4.

$$-16\times 4+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

Multiply -16 and 4 to get -64.

$$-64+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-64+\sqrt[3]{-64}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-64-4\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-64-4\times \frac{1}{4}-\sqrt[3]{27}$$

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

$$-64-1-\sqrt[3]{27}$$

Subtract 1 from -64 to get -65.

$$-65-\sqrt[3]{27}$$

Calculate \sqrt[3]{27} and get 3.

$$-65-3$$

Subtract 3 from -65 to get -68.

$$-68$$

Factor

$$-68$$