Solve (-9/14-4:14/3)^2+(-21)(-3)^-2+4/9-frac{2/9:frac{6}{11}}{(-frac{1}{6}-frac{5}{4}-frac{1}{12})^-2}

$$( - \frac { 9 } { 14 } - 4 : \frac { 14 } { 3 } ) ^ { 2 } + ( - 21 ) ( - 3 ) ^ { - 2 } + \frac { \frac { 4 } { 9 } - \frac { 2 } { 9 } : \frac { 6 } { 11 } } { ( - \frac { 1 } { 6 } - \frac { 5 } { 4 } - \frac { 1 } { 12 } ) ^ { - 2 } }$$

Evaluate

$$0$$

Solution Steps

Divide 4 by \frac{14}{3} by multiplying 4 by the reciprocal of \frac{14}{3}.

$$\left(-\frac{9}{14}-4\times \frac{3}{14}\right)^{2}-21\left(-3\right)^{-2}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Multiply 4 and \frac{3}{14} to get \frac{6}{7}.

$$\left(-\frac{9}{14}-\frac{6}{7}\right)^{2}-21\left(-3\right)^{-2}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Subtract \frac{6}{7} from -\frac{9}{14} to get -\frac{3}{2}.

$$\left(-\frac{3}{2}\right)^{2}-21\left(-3\right)^{-2}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Calculate -\frac{3}{2} to the power of 2 and get \frac{9}{4}.

$$\frac{9}{4}-21\left(-3\right)^{-2}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Calculate -3 to the power of -2 and get \frac{1}{9}.

$$\frac{9}{4}-21\times \frac{1}{9}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Multiply -21 and \frac{1}{9} to get -\frac{7}{3}.

$$\frac{9}{4}-\frac{7}{3}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Subtract \frac{7}{3} from \frac{9}{4} to get -\frac{1}{12}.

$$-\frac{1}{12}+\frac{\frac{4}{9}-\frac{\frac{2}{9}}{\frac{6}{11}}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Divide \frac{2}{9} by \frac{6}{11} by multiplying \frac{2}{9} by the reciprocal of \frac{6}{11}.

$$-\frac{1}{12}+\frac{\frac{4}{9}-\frac{2}{9}\times \frac{11}{6}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Multiply \frac{2}{9} and \frac{11}{6} to get \frac{11}{27}.

$$-\frac{1}{12}+\frac{\frac{4}{9}-\frac{11}{27}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Subtract \frac{11}{27} from \frac{4}{9} to get \frac{1}{27}.

$$-\frac{1}{12}+\frac{\frac{1}{27}}{\left(-\frac{1}{6}-\frac{5}{4}-\frac{1}{12}\right)^{-2}}$$

Subtract \frac{5}{4} from -\frac{1}{6} to get -\frac{17}{12}.

$$-\frac{1}{12}+\frac{\frac{1}{27}}{\left(-\frac{17}{12}-\frac{1}{12}\right)^{-2}}$$

Subtract \frac{1}{12} from -\frac{17}{12} to get -\frac{3}{2}.

$$-\frac{1}{12}+\frac{\frac{1}{27}}{\left(-\frac{3}{2}\right)^{-2}}$$

Calculate -\frac{3}{2} to the power of -2 and get \frac{4}{9}.

$$-\frac{1}{12}+\frac{\frac{1}{27}}{\frac{4}{9}}$$

Divide \frac{1}{27} by \frac{4}{9} by multiplying \frac{1}{27} by the reciprocal of \frac{4}{9}.

$$-\frac{1}{12}+\frac{1}{27}\times \frac{9}{4}$$

Multiply \frac{1}{27} and \frac{9}{4} to get \frac{1}{12}.

$$-\frac{1}{12}+\frac{1}{12}$$

Add -\frac{1}{12} and \frac{1}{12} to get 0.

$$0$$

Factor

$$0$$