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

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

Evaluate

$$\frac{151}{144}\approx 1.048611111$$

Solution Steps

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

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

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

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

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

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

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

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

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

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

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

$$\frac{25}{64}\times \frac{4}{9}+\left(\frac{1}{2}\right)^{2}\left(2+\frac{1}{4}\right)-\left(\frac{1}{4}\right)^{2}\left(4-3^{2}\right)$$

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

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

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

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

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

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

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

$$\frac{25}{144}+\frac{9}{16}-\left(\frac{1}{4}\right)^{2}\left(4-3^{2}\right)$$

Add \frac{25}{144} and \frac{9}{16} to get \frac{53}{72}.

$$\frac{53}{72}-\left(\frac{1}{4}\right)^{2}\left(4-3^{2}\right)$$

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

$$\frac{53}{72}-\frac{1}{16}\left(4-3^{2}\right)$$

Calculate 3 to the power of 2 and get 9.

$$\frac{53}{72}-\frac{1}{16}\left(4-9\right)$$

Subtract 9 from 4 to get -5.

$$\frac{53}{72}-\frac{1}{16}\left(-5\right)$$

Multiply \frac{1}{16} and -5 to get -\frac{5}{16}.

$$\frac{53}{72}-\left(-\frac{5}{16}\right)$$

The opposite of -\frac{5}{16} is \frac{5}{16}.

$$\frac{53}{72}+\frac{5}{16}$$

Add \frac{53}{72} and \frac{5}{16} to get \frac{151}{144}.

$$\frac{151}{144}$$

Factor

$$\frac{151}{2 ^ {4} \cdot 3 ^ {2}} = 1\frac{7}{144} = 1.0486111111111112$$