Solve (1+3/5):(3-3/5)^2-(1-1/4)^2*(-1+1/3)^4

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

Evaluate

$$\frac{1}{6}\approx 0.166666667$$

Solution Steps

Add 1 and \frac{3}{5} to get \frac{8}{5}.

$$\frac{\frac{8}{5}}{\left(3-\frac{3}{5}\right)^{2}}-\left(1-\frac{1}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

Subtract \frac{3}{5} from 3 to get \frac{12}{5}.

$$\frac{\frac{8}{5}}{\left(\frac{12}{5}\right)^{2}}-\left(1-\frac{1}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

Calculate \frac{12}{5} to the power of 2 and get \frac{144}{25}.

$$\frac{\frac{8}{5}}{\frac{144}{25}}-\left(1-\frac{1}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

Divide \frac{8}{5} by \frac{144}{25} by multiplying \frac{8}{5} by the reciprocal of \frac{144}{25}.

$$\frac{8}{5}\times \frac{25}{144}-\left(1-\frac{1}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

Multiply \frac{8}{5} and \frac{25}{144} to get \frac{5}{18}.

$$\frac{5}{18}-\left(1-\frac{1}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

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

$$\frac{5}{18}-\left(\frac{3}{4}\right)^{2}\left(-1+\frac{1}{3}\right)^{4}$$

Calculate \frac{3}{4} to the power of 2 and get \frac{9}{16}.

$$\frac{5}{18}-\frac{9}{16}\left(-1+\frac{1}{3}\right)^{4}$$

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

$$\frac{5}{18}-\frac{9}{16}\left(-\frac{2}{3}\right)^{4}$$

Calculate -\frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{5}{18}-\frac{9}{16}\times \frac{16}{81}$$

Multiply \frac{9}{16} and \frac{16}{81} to get \frac{1}{9}.

$$\frac{5}{18}-\frac{1}{9}$$

Subtract \frac{1}{9} from \frac{5}{18} to get \frac{1}{6}.

$$\frac{1}{6}$$

Factor

$$\frac{1}{2 \cdot 3} = 0.16666666666666666$$