Solve 3/7{4/frac{8{{left(frac{2/6^right)}^2}}}}

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

Evaluate

$$\frac{1}{42}\approx 0.023809524$$

Solution Steps

Divide 3 by \frac{7}{\frac{4}{\frac{8}{\left(\frac{2}{6^{1}}\right)^{2}}}} by multiplying 3 by the reciprocal of \frac{7}{\frac{4}{\frac{8}{\left(\frac{2}{6^{1}}\right)^{2}}}}.

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

Divide 4 by \frac{8}{\left(\frac{2}{6^{1}}\right)^{2}} by multiplying 4 by the reciprocal of \frac{8}{\left(\frac{2}{6^{1}}\right)^{2}}.

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

Calculate 6 to the power of 1 and get 6.

$$\frac{3\times \frac{4\times \left(\frac{2}{6}\right)^{2}}{8}}{7}$$

Reduce the fraction \frac{2}{6} to lowest terms by extracting and canceling out 2.

$$\frac{3\times \frac{4\times \left(\frac{1}{3}\right)^{2}}{8}}{7}$$

Calculate \frac{1}{3} to the power of 2 and get \frac{1}{9}.

$$\frac{3\times \frac{4\times \frac{1}{9}}{8}}{7}$$

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

$$\frac{3\times \frac{\frac{4}{9}}{8}}{7}$$

Express \frac{\frac{4}{9}}{8} as a single fraction.

$$\frac{3\times \frac{4}{9\times 8}}{7}$$

Multiply 9 and 8 to get 72.

$$\frac{3\times \frac{4}{72}}{7}$$

Reduce the fraction \frac{4}{72} to lowest terms by extracting and canceling out 4.

$$\frac{3\times \frac{1}{18}}{7}$$

Multiply 3 and \frac{1}{18} to get \frac{1}{6}.

$$\frac{\frac{1}{6}}{7}$$

Express \frac{\frac{1}{6}}{7} as a single fraction.

$$\frac{1}{6\times 7}$$

Multiply 6 and 7 to get 42.

$$\frac{1}{42}$$

Factor

$$\frac{1}{2 \cdot 3 \cdot 7} = 0.023809523809523808$$