Solve sqrt{[(3/2-1/3):(2-1/4)-(1/3-frac{1}{4})]:(frac{3}{7}-frac{2}{21})}^0,01

$$\sqrt { [ ( \frac { 3 } { 2 } - \frac { 1 } { 3 } ) : ( 2 - \frac { 1 } { 4 } ) - ( \frac { 1 } { 3 } - \frac { 1 } { 4 } ) ] : ( \frac { 3 } { 7 } - \frac { 2 } { 21 } ) } ^ { 0,01 }$$

Evaluate

$$\frac{4^{0,995}\sqrt[200]{7}}{4}\approx 1.002801997$$

Solution Steps

Subtract \frac{1}{3} from \frac{3}{2} to get \frac{7}{6}.

$$\left(\sqrt{\frac{\frac{\frac{7}{6}}{2-\frac{1}{4}}-\left(\frac{1}{3}-\frac{1}{4}\right)}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

Subtract \frac{1}{4} from 2 to get \frac{7}{4}.

$$\left(\sqrt{\frac{\frac{\frac{7}{6}}{\frac{7}{4}}-\left(\frac{1}{3}-\frac{1}{4}\right)}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

Divide \frac{7}{6} by \frac{7}{4} by multiplying \frac{7}{6} by the reciprocal of \frac{7}{4}.

$$\left(\sqrt{\frac{\frac{7}{6}\times \frac{4}{7}-\left(\frac{1}{3}-\frac{1}{4}\right)}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

Multiply \frac{7}{6} and \frac{4}{7} to get \frac{2}{3}.

$$\left(\sqrt{\frac{\frac{2}{3}-\left(\frac{1}{3}-\frac{1}{4}\right)}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

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

$$\left(\sqrt{\frac{\frac{2}{3}-\frac{1}{12}}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

Subtract \frac{1}{12} from \frac{2}{3} to get \frac{7}{12}.

$$\left(\sqrt{\frac{\frac{7}{12}}{\frac{3}{7}-\frac{2}{21}}}\right)^{0,01}$$

Subtract \frac{2}{21} from \frac{3}{7} to get \frac{1}{3}.

$$\left(\sqrt{\frac{\frac{7}{12}}{\frac{1}{3}}}\right)^{0,01}$$

Divide \frac{7}{12} by \frac{1}{3} by multiplying \frac{7}{12} by the reciprocal of \frac{1}{3}.

$$\left(\sqrt{\frac{7}{12}\times 3}\right)^{0,01}$$

Multiply \frac{7}{12} and 3 to get \frac{7}{4}.

$$\left(\sqrt{\frac{7}{4}}\right)^{0,01}$$