Solve (2/3)^2:{1/3-(2/3)^2:[(1+4/9)+frac{7}{3}:(3+6*frac{1}{5})]^2}

$$( \frac { 2 } { 3 } ) ^ { 2 } : \{ \frac { 1 } { 3 } - ( \frac { 2 } { 3 } ) ^ { 2 } : [ ( 1 + \frac { 4 } { 9 } ) + \frac { 7 } { 3 } : ( 3 + 6 \cdot \frac { 1 } { 5 } ) ] ^ { 2 } \}$$

Evaluate

$$2$$

Solution Steps

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

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

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

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

Add 1 and \frac{4}{9} to get \frac{13}{9}.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{\left(\frac{13}{9}+\frac{\frac{7}{3}}{3+6\times \frac{1}{5}}\right)^{2}}}$$

Multiply 6 and \frac{1}{5} to get \frac{6}{5}.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{\left(\frac{13}{9}+\frac{\frac{7}{3}}{3+\frac{6}{5}}\right)^{2}}}$$

Add 3 and \frac{6}{5} to get \frac{21}{5}.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{\left(\frac{13}{9}+\frac{\frac{7}{3}}{\frac{21}{5}}\right)^{2}}}$$

Divide \frac{7}{3} by \frac{21}{5} by multiplying \frac{7}{3} by the reciprocal of \frac{21}{5}.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{\left(\frac{13}{9}+\frac{7}{3}\times \frac{5}{21}\right)^{2}}}$$

Multiply \frac{7}{3} and \frac{5}{21} to get \frac{5}{9}.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{\left(\frac{13}{9}+\frac{5}{9}\right)^{2}}}$$

Add \frac{13}{9} and \frac{5}{9} to get 2.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{2^{2}}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{\frac{4}{9}}{4}}$$

Express \frac{\frac{4}{9}}{4} as a single fraction.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{4}{9\times 4}}$$

Cancel out 4 in both numerator and denominator.

$$\frac{\frac{4}{9}}{\frac{1}{3}-\frac{1}{9}}$$

Subtract \frac{1}{9} from \frac{1}{3} to get \frac{2}{9}.

$$\frac{\frac{4}{9}}{\frac{2}{9}}$$

Divide \frac{4}{9} by \frac{2}{9} by multiplying \frac{4}{9} by the reciprocal of \frac{2}{9}.

$$\frac{4}{9}\times \frac{9}{2}$$

Multiply \frac{4}{9} and \frac{9}{2} to get 2.

$$2$$

Factor

$$2$$