Solve (3+2/3+3{4+frac{2/3}})^2div(2-0/1-5{9-frac{3/2}})^-2

$$( 3 + \frac { 2 } { 3 + \frac { 3 } { 4 + \frac { 2 } { 3 } } } ) ^ { 2 } \div ( 2 - \frac { 0 } { 1 - \frac { 5 } { 9 - \frac { 3 } { 2 } } } ) ^ { - 2 }$$

Evaluate

$$\frac{131044}{2601}\approx 50.382160707$$

Solution Steps

Add 4 and \frac{2}{3} to get \frac{14}{3}.

$$\frac{\left(3+\frac{2}{3+\frac{3}{\frac{14}{3}}}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

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

$$\frac{\left(3+\frac{2}{3+3\times \frac{3}{14}}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Multiply 3 and \frac{3}{14} to get \frac{9}{14}.

$$\frac{\left(3+\frac{2}{3+\frac{9}{14}}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Add 3 and \frac{9}{14} to get \frac{51}{14}.

$$\frac{\left(3+\frac{2}{\frac{51}{14}}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Divide 2 by \frac{51}{14} by multiplying 2 by the reciprocal of \frac{51}{14}.

$$\frac{\left(3+2\times \frac{14}{51}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Multiply 2 and \frac{14}{51} to get \frac{28}{51}.

$$\frac{\left(3+\frac{28}{51}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Add 3 and \frac{28}{51} to get \frac{181}{51}.

$$\frac{\left(\frac{181}{51}\right)^{2}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Calculate \frac{181}{51} to the power of 2 and get \frac{32761}{2601}.

$$\frac{\frac{32761}{2601}}{\left(2-\frac{0}{1-\frac{5}{9-\frac{3}{2}}}\right)^{-2}}$$

Subtract \frac{3}{2} from 9 to get \frac{15}{2}.

$$\frac{\frac{32761}{2601}}{\left(2-\frac{0}{1-\frac{5}{\frac{15}{2}}}\right)^{-2}}$$

Divide 5 by \frac{15}{2} by multiplying 5 by the reciprocal of \frac{15}{2}.

$$\frac{\frac{32761}{2601}}{\left(2-\frac{0}{1-5\times \frac{2}{15}}\right)^{-2}}$$

Multiply 5 and \frac{2}{15} to get \frac{2}{3}.

$$\frac{\frac{32761}{2601}}{\left(2-\frac{0}{1-\frac{2}{3}}\right)^{-2}}$$

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

$$\frac{\frac{32761}{2601}}{\left(2-\frac{0}{\frac{1}{3}}\right)^{-2}}$$

Zero divided by any non-zero number gives zero.

$$\frac{\frac{32761}{2601}}{\left(2+0\right)^{-2}}$$

Add 2 and 0 to get 2.

$$\frac{\frac{32761}{2601}}{2^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{32761}{2601}}{\frac{1}{4}}$$

Divide \frac{32761}{2601} by \frac{1}{4} by multiplying \frac{32761}{2601} by the reciprocal of \frac{1}{4}.

$$\frac{32761}{2601}\times 4$$

Multiply \frac{32761}{2601} and 4 to get \frac{131044}{2601}.

$$\frac{131044}{2601}$$

Factor

$$\frac{2 ^ {2} \cdot 181 ^ {2}}{3 ^ {2} \cdot 17 ^ {2}} = 50\frac{994}{2601} = 50.382160707420226$$