Solve (-2)^3*sqrt{(-4)^2}+sqrt[3]{(-4)^3}*(1/2)^2-sqrt[4]{81}

$$( - 2 ) ^ { 3 } \times \sqrt { ( - 4 ) ^ { 2 } } + \sqrt[ 3 ] { ( - 4 ) ^ { 3 } } \times ( \frac { 1 } { 2 } ) ^ { 2 } - \sqrt[ 4 ] { 81 }$$

Evaluate

$$-36$$

Solution Steps

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

$$-8\sqrt{\left(-4\right)^{2}}+\sqrt[3]{\left(-4\right)^{3}}\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

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

$$-8\sqrt{16}+\sqrt[3]{\left(-4\right)^{3}}\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

Calculate the square root of 16 and get 4.

$$-8\times 4+\sqrt[3]{\left(-4\right)^{3}}\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

Multiply -8 and 4 to get -32.

$$-32+\sqrt[3]{\left(-4\right)^{3}}\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

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

$$-32+\sqrt[3]{-64}\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

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

$$-32-4\times \left(\frac{1}{2}\right)^{2}-\sqrt[4]{81}$$

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

$$-32-4\times \frac{1}{4}-\sqrt[4]{81}$$

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

$$-32-1-\sqrt[4]{81}$$

Subtract 1 from -32 to get -33.

$$-33-\sqrt[4]{81}$$

Calculate \sqrt[4]{81} and get 3.

$$-33-3$$

Subtract 3 from -33 to get -36.

$$-36$$

Factor

$$-36$$