Solve [(1/21/4frac{1/8)^frac{1{6}}}{1-1/2}]-frac{-2+2:frac{4}{3}}{1-1:frac{2}{3}}+sqrt{frac{2-frac{2}{3}}{frac{1}{3}-frac{1}{4}}}=

$$[ \frac { ( \frac { 1 } { 2 } \frac { 1 } { 4 } \frac { 1 } { 8 } ) ^ { \frac { 1 } { 6 } } } { 1 - \frac { 1 } { 2 } } ] - \frac { - 2 + 2 : \frac { 4 } { 3 } } { 1 - 1 : \frac { 2 } { 3 } } + \sqrt { \frac { 2 - \frac { 2 } { 3 } } { \frac { 1 } { 3 } - \frac { 1 } { 4 } } } =$$

Evaluate

$$4$$

Solution Steps

Multiply \frac{1}{2} and \frac{1}{4} to get \frac{1}{8}.

$$\frac{\left(\frac{1}{8}\times \frac{1}{8}\right)^{\frac{1}{6}}}{1-\frac{1}{2}}-\frac{-2+\frac{2}{\frac{4}{3}}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Multiply \frac{1}{8} and \frac{1}{8} to get \frac{1}{64}.

$$\frac{\left(\frac{1}{64}\right)^{\frac{1}{6}}}{1-\frac{1}{2}}-\frac{-2+\frac{2}{\frac{4}{3}}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Calculate \frac{1}{64} to the power of \frac{1}{6} and get \frac{1}{2}.

$$\frac{\frac{1}{2}}{1-\frac{1}{2}}-\frac{-2+\frac{2}{\frac{4}{3}}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{\frac{1}{2}}{\frac{1}{2}}-\frac{-2+\frac{2}{\frac{4}{3}}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Divide \frac{1}{2} by \frac{1}{2} to get 1.

$$1-\frac{-2+\frac{2}{\frac{4}{3}}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Divide 2 by \frac{4}{3} by multiplying 2 by the reciprocal of \frac{4}{3}.

$$1-\frac{-2+2\times \frac{3}{4}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Multiply 2 and \frac{3}{4} to get \frac{3}{2}.

$$1-\frac{-2+\frac{3}{2}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Add -2 and \frac{3}{2} to get -\frac{1}{2}.

$$1-\frac{-\frac{1}{2}}{1-\frac{1}{\frac{2}{3}}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Divide 1 by \frac{2}{3} by multiplying 1 by the reciprocal of \frac{2}{3}.

$$1-\frac{-\frac{1}{2}}{1-1\times \frac{3}{2}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Multiply 1 and \frac{3}{2} to get \frac{3}{2}.

$$1-\frac{-\frac{1}{2}}{1-\frac{3}{2}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

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

$$1-\frac{-\frac{1}{2}}{-\frac{1}{2}}+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Divide -\frac{1}{2} by -\frac{1}{2} to get 1.

$$1-1+\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Subtract 1 from 1 to get 0.

$$\sqrt{\frac{2-\frac{2}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

Subtract \frac{2}{3} from 2 to get \frac{4}{3}.

$$\sqrt{\frac{\frac{4}{3}}{\frac{1}{3}-\frac{1}{4}}}$$

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

$$\sqrt{\frac{\frac{4}{3}}{\frac{1}{12}}}$$

Divide \frac{4}{3} by \frac{1}{12} by multiplying \frac{4}{3} by the reciprocal of \frac{1}{12}.

$$\sqrt{\frac{4}{3}\times 12}$$

Multiply \frac{4}{3} and 12 to get 16.

$$\sqrt{16}$$

Calculate the square root of 16 and get 4.

$$4$$

Factor

$$2^{2}$$