Solve -1^2-(-2)^3*1/8-sqrt[3]{27}*|-1/3|+2div(sqrt{2})^2

$$- 1 ^ { 2 } - ( - 2 ) ^ { 3 } \times \frac { 1 } { 8 } - \sqrt[ 3 ] { 27 } \times | - \frac { 1 } { 3 } | + 2 \div ( \sqrt { 2 } ) ^ { 2 }$$

Evaluate

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Solution Steps

Calculate 1 to the power of 2 and get 1.

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

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

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

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

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

The opposite of -1 is 1.

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

Add -1 and 1 to get 0.

$$0-\sqrt[3]{27}|-\frac{1}{3}|+\frac{2}{\left(\sqrt{2}\right)^{2}}$$

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

$$0-3|-\frac{1}{3}|+\frac{2}{\left(\sqrt{2}\right)^{2}}$$

The absolute value of a real number a is a when a\geq 0, or -a when a<0. The absolute value of -\frac{1}{3} is \frac{1}{3}.

$$0-3\times \frac{1}{3}+\frac{2}{\left(\sqrt{2}\right)^{2}}$$

Multiply 3 and \frac{1}{3} to get 1.

$$0-1+\frac{2}{\left(\sqrt{2}\right)^{2}}$$

Subtract 1 from 0 to get -1.

$$-1+\frac{2}{\left(\sqrt{2}\right)^{2}}$$

The square of \sqrt{2} is 2.

$$-1+\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$-1+1$$

Add -1 and 1 to get 0.

$$0$$

Factor

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