Solve [(2-13/5)^2+(5/8-3/4)^4*(7-1/3)^3]+(5-frac{6}{5})

$$[ ( 2 - 1 \frac { 3 } { 5 } ) ^ { 2 } + ( \frac { 5 } { 8 } - \frac { 3 } { 4 } ) ^ { 4 } \times ( 7 - \frac { 1 } { 3 } ) ^ { 3 } ] + ( 5 - \frac { 6 } { 5 } )$$

Evaluate

$$\frac{174197}{43200}\approx 4.032337963$$

Solution Steps

Multiply 1 and 5 to get 5.

$$\left(2-\frac{5+3}{5}\right)^{2}+\left(\frac{5}{8}-\frac{3}{4}\right)^{4}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Add 5 and 3 to get 8.

$$\left(2-\frac{8}{5}\right)^{2}+\left(\frac{5}{8}-\frac{3}{4}\right)^{4}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Subtract \frac{8}{5} from 2 to get \frac{2}{5}.

$$\left(\frac{2}{5}\right)^{2}+\left(\frac{5}{8}-\frac{3}{4}\right)^{4}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Calculate \frac{2}{5} to the power of 2 and get \frac{4}{25}.

$$\frac{4}{25}+\left(\frac{5}{8}-\frac{3}{4}\right)^{4}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Subtract \frac{3}{4} from \frac{5}{8} to get -\frac{1}{8}.

$$\frac{4}{25}+\left(-\frac{1}{8}\right)^{4}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Calculate -\frac{1}{8} to the power of 4 and get \frac{1}{4096}.

$$\frac{4}{25}+\frac{1}{4096}\left(7-\frac{1}{3}\right)^{3}+5-\frac{6}{5}$$

Subtract \frac{1}{3} from 7 to get \frac{20}{3}.

$$\frac{4}{25}+\frac{1}{4096}\times \left(\frac{20}{3}\right)^{3}+5-\frac{6}{5}$$

Calculate \frac{20}{3} to the power of 3 and get \frac{8000}{27}.

$$\frac{4}{25}+\frac{1}{4096}\times \frac{8000}{27}+5-\frac{6}{5}$$

Multiply \frac{1}{4096} and \frac{8000}{27} to get \frac{125}{1728}.

$$\frac{4}{25}+\frac{125}{1728}+5-\frac{6}{5}$$

Add \frac{4}{25} and \frac{125}{1728} to get \frac{10037}{43200}.

$$\frac{10037}{43200}+5-\frac{6}{5}$$

Add \frac{10037}{43200} and 5 to get \frac{226037}{43200}.

$$\frac{226037}{43200}-\frac{6}{5}$$

Subtract \frac{6}{5} from \frac{226037}{43200} to get \frac{174197}{43200}.

$$\frac{174197}{43200}$$

Factor

$$\frac{174197}{2 ^ {6} \cdot 3 ^ {3} \cdot 5 ^ {2}} = 4\frac{1397}{43200} = 4.032337962962963$$