Solve {l}{sqrt{1/81}+sqrt[3]{-27}}{+sqrt{(-2)^2}}{+(-1)^2014}

$$\left. \begin{array} { l } { \sqrt { \frac { 1 } { 81 } } + \sqrt[ 3 ] { - 27 } } \\ { + \sqrt { ( - 2 ) ^ { 2 } } } \\ { + ( - 1 ) ^ { 2014 } } \end{array} \right.$$

Evaluate

$$\frac{1}{9}\approx 0.111111111$$

Solution Steps

Rewrite the square root of the division \frac{1}{81} as the division of square roots \frac{\sqrt{1}}{\sqrt{81}}. Take the square root of both numerator and denominator.

$$\frac{1}{9}+\sqrt[3]{-27}+\sqrt{\left(-2\right)^{2}}+\left(-1\right)^{2014}$$

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

$$\frac{1}{9}-3+\sqrt{\left(-2\right)^{2}}+\left(-1\right)^{2014}$$

Subtract 3 from \frac{1}{9} to get -\frac{26}{9}.

$$-\frac{26}{9}+\sqrt{\left(-2\right)^{2}}+\left(-1\right)^{2014}$$

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

$$-\frac{26}{9}+\sqrt{4}+\left(-1\right)^{2014}$$

Calculate the square root of 4 and get 2.

$$-\frac{26}{9}+2+\left(-1\right)^{2014}$$

Add -\frac{26}{9} and 2 to get -\frac{8}{9}.

$$-\frac{8}{9}+\left(-1\right)^{2014}$$

Calculate -1 to the power of 2014 and get 1.

$$-\frac{8}{9}+1$$

Add -\frac{8}{9} and 1 to get \frac{1}{9}.

$$\frac{1}{9}$$

Factor

$$\frac{1}{3 ^ {2}} = 0.1111111111111111$$