Solve (-1+3/2)^4div[(-2+3/4)^3div(-5/2)^3]-(-1+2/3-frac{1}{6})^2

$$( - 1 + \frac { 3 } { 2 } ) ^ { 4 } \div [ ( - 2 + \frac { 3 } { 4 } ) ^ { 3 } \div ( \frac { - 5 } { 2 } ) ^ { 3 } ] - ( - 1 + \frac { 2 } { 3 } - \frac { 1 } { 6 } ) ^ { 2 }$$

Evaluate

$$\frac{1}{4}=0.25$$

Solution Steps

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

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

Calculate \frac{1}{2} to the power of 4 and get \frac{1}{16}.

$$\frac{\frac{1}{16}}{\frac{\left(-2+\frac{3}{4}\right)^{3}}{\left(\frac{-5}{2}\right)^{3}}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Add -2 and \frac{3}{4} to get -\frac{5}{4}.

$$\frac{\frac{1}{16}}{\frac{\left(-\frac{5}{4}\right)^{3}}{\left(\frac{-5}{2}\right)^{3}}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Calculate -\frac{5}{4} to the power of 3 and get -\frac{125}{64}.

$$\frac{\frac{1}{16}}{\frac{-\frac{125}{64}}{\left(\frac{-5}{2}\right)^{3}}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Fraction \frac{-5}{2} can be rewritten as -\frac{5}{2} by extracting the negative sign.

$$\frac{\frac{1}{16}}{\frac{-\frac{125}{64}}{\left(-\frac{5}{2}\right)^{3}}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Calculate -\frac{5}{2} to the power of 3 and get -\frac{125}{8}.

$$\frac{\frac{1}{16}}{\frac{-\frac{125}{64}}{-\frac{125}{8}}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Divide -\frac{125}{64} by -\frac{125}{8} by multiplying -\frac{125}{64} by the reciprocal of -\frac{125}{8}.

$$\frac{\frac{1}{16}}{-\frac{125}{64}\left(-\frac{8}{125}\right)}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Multiply -\frac{125}{64} and -\frac{8}{125} to get \frac{1}{8}.

$$\frac{\frac{1}{16}}{\frac{1}{8}}-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Divide \frac{1}{16} by \frac{1}{8} by multiplying \frac{1}{16} by the reciprocal of \frac{1}{8}.

$$\frac{1}{16}\times 8-\left(-1+\frac{2}{3}-\frac{1}{6}\right)^{2}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

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

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

$$\frac{1}{2}-\left(-\frac{1}{3}-\frac{1}{6}\right)^{2}$$

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

$$\frac{1}{2}-\left(-\frac{1}{2}\right)^{2}$$

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

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

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

$$\frac{1}{4}$$

Factor

$$\frac{1}{2 ^ {2}} = 0.25$$