Solve {left(8/4-3/2right)}^2+{left(1/6right)}^2-3^2/4^2divfrac{7}{3}

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

Evaluate

$$\frac{37}{1008}\approx 0.036706349$$

Solution Steps

Divide 8 by 4 to get 2.

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

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

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

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

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

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{1}{4}+\frac{1}{36}-\frac{\frac{3^{2}}{4^{2}}}{\frac{7}{3}}$$

Add \frac{1}{4} and \frac{1}{36} to get \frac{5}{18}.

$$\frac{5}{18}-\frac{\frac{3^{2}}{4^{2}}}{\frac{7}{3}}$$

Divide \frac{3^{2}}{4^{2}} by \frac{7}{3} by multiplying \frac{3^{2}}{4^{2}} by the reciprocal of \frac{7}{3}.

$$\frac{5}{18}-\frac{3^{2}\times 3}{4^{2}\times 7}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{5}{18}-\frac{3^{3}}{4^{2}\times 7}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{5}{18}-\frac{27}{4^{2}\times 7}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{5}{18}-\frac{27}{16\times 7}$$

Multiply 16 and 7 to get 112.

$$\frac{5}{18}-\frac{27}{112}$$

Subtract \frac{27}{112} from \frac{5}{18} to get \frac{37}{1008}.

$$\frac{37}{1008}$$

Factor

$$\frac{37}{2 ^ {4} \cdot 3 ^ {2} \cdot 7} = 0.03670634920634921$$