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

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

Evaluate

$$-36$$

Solution Steps

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

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

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

$$-8\sqrt{16}+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

Calculate the square root of 16 and get 4.

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

Multiply -8 and 4 to get -32.

$$-32+\sqrt[3]{\left(-4\right)^{3}}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-32+\sqrt[3]{-64}\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-32-4\left(-\frac{1}{2}\right)^{2}-\sqrt[3]{27}$$

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

$$-32-4\times \frac{1}{4}-\sqrt[3]{27}$$

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

$$-32-1-\sqrt[3]{27}$$

Subtract 1 from -32 to get -33.

$$-33-\sqrt[3]{27}$$

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

$$-33-3$$

Subtract 3 from -33 to get -36.

$$-36$$

Factor

$$-36$$