Solve {left(1/3+7/6right)}^{2}{left(2/3-1/4right)}^2{left(frac{2}{5}right)}^2+{left(frac{1}{2}right)}^2left(2+frac{1}{4}right)-{left(frac{1}{1}right)}^2left(4-3^2right)

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

Evaluate

$$\frac{45}{8}=5.625$$

Solution Steps

Divide 1 by 1 to get 1.

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

Add \frac{1}{3} and \frac{7}{6} to get \frac{3}{2}.

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

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

$$\frac{9}{4}\left(\frac{2}{3}-\frac{1}{4}\right)^{2}\times \left(\frac{2}{5}\right)^{2}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-1^{2}\left(4-3^{2}\right)$$

Subtract \frac{1}{4} from \frac{2}{3} to get \frac{5}{12}.

$$\frac{9}{4}\times \left(\frac{5}{12}\right)^{2}\times \left(\frac{2}{5}\right)^{2}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-1^{2}\left(4-3^{2}\right)$$

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

$$\frac{9}{4}\times \frac{25}{144}\times \left(\frac{2}{5}\right)^{2}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-1^{2}\left(4-3^{2}\right)$$

Multiply \frac{9}{4} and \frac{25}{144} to get \frac{25}{64}.

$$\frac{25}{64}\times \left(\frac{2}{5}\right)^{2}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-1^{2}\left(4-3^{2}\right)$$

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

$$\frac{25}{64}\times \frac{4}{25}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-1^{2}\left(4-3^{2}\right)$$

Multiply \frac{25}{64} and \frac{4}{25} to get \frac{1}{16}.

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

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

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

Add 2 and \frac{1}{4} to get \frac{9}{4}.

$$\frac{1}{16}+\frac{1}{4}\times \frac{9}{4}-1^{2}\left(4-3^{2}\right)$$

Multiply \frac{1}{4} and \frac{9}{4} to get \frac{9}{16}.

$$\frac{1}{16}+\frac{9}{16}-1^{2}\left(4-3^{2}\right)$$

Add \frac{1}{16} and \frac{9}{16} to get \frac{5}{8}.

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

Calculate 1 to the power of 2 and get 1.

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

Calculate 3 to the power of 2 and get 9.

$$\frac{5}{8}-1\left(4-9\right)$$

Subtract 9 from 4 to get -5.

$$\frac{5}{8}-1\left(-5\right)$$

Multiply 1 and -5 to get -5.

$$\frac{5}{8}-\left(-5\right)$$

The opposite of -5 is 5.

$$\frac{5}{8}+5$$

Add \frac{5}{8} and 5 to get \frac{45}{8}.

$$\frac{45}{8}$$

Factor

$$\frac{3 ^ {2} \cdot 5}{2 ^ {3}} = 5\frac{5}{8} = 5.625$$