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

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

Evaluate

$$40$$

Solution Steps

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

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

Subtract 4 from 2 to get -2.

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

Calculate -1 to the power of -5 and get -1.

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

Subtract 1 from -3 to get -4.

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

Reduce the fraction \frac{-2}{-4} to lowest terms by extracting and canceling out -2.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

Subtract \frac{3}{4} from \frac{5}{4} to get \frac{1}{2}.

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

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

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

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

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

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

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

Add \frac{1}{4} and \frac{1}{4} to get \frac{1}{2}.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$2+4\times 9+\frac{\frac{\frac{2}{3}-1}{1-\frac{2}{3}}}{\frac{3}{2}-2}$$

Multiply 4 and 9 to get 36.

$$2+36+\frac{\frac{\frac{2}{3}-1}{1-\frac{2}{3}}}{\frac{3}{2}-2}$$

Add 2 and 36 to get 38.

$$38+\frac{\frac{\frac{2}{3}-1}{1-\frac{2}{3}}}{\frac{3}{2}-2}$$

Extract the negative sign in \frac{2}{3}-1.

$$38+\frac{\frac{-\left(1-\frac{2}{3}\right)}{1-\frac{2}{3}}}{\frac{3}{2}-2}$$

Cancel out 1-\frac{2}{3} in both numerator and denominator.

$$38+\frac{-1}{\frac{3}{2}-2}$$

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

$$38+\frac{-1}{-\frac{1}{2}}$$

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

$$38-\left(-2\right)$$

Multiply -1 and -2 to get 2.

$$38+2$$

Add 38 and 2 to get 40.

$$40$$

Factor

$$2^{3}\times 5$$