Solve frac{frac{frac{frac{5/6/6/2.2/8}{28.5}}{8}}{5}}{5}

$$\frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ \frac{ 5 }{ 6 } }{ 6 } }{ 2.2 } }{ 8 } }{ 28.5 } }{ 8 } }{ 5 } }{ 5 }$$

Evaluate

$$\frac{1}{722304}\approx 0.000001384$$

Solution Steps

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{5}{6}}{6}}{2.2}}{8}}{28.5}}{8}}{5}}{5} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{5}{6}}{6}}{2.2}}{8}}{28.5}}{8}}{5\times 5}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{5}{6}}{6}}{2.2}}{8}}{28.5}}{8} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{5}{6}}{6}}{2.2}}{8}}{28.5\times 8}}{5\times 5}$$

Express \frac{\frac{\frac{\frac{5}{6}}{6}}{2.2}}{8} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{5}{6}}{6}}{2.2\times 8}}{28.5\times 8}}{5\times 5}$$

Express \frac{\frac{5}{6}}{6} as a single fraction.

$$\frac{\frac{\frac{\frac{5}{6\times 6}}{2.2\times 8}}{28.5\times 8}}{5\times 5}$$

Multiply 6 and 6 to get 36.

$$\frac{\frac{\frac{\frac{5}{36}}{2.2\times 8}}{28.5\times 8}}{5\times 5}$$

Multiply 2.2 and 8 to get 17.6.

$$\frac{\frac{\frac{\frac{5}{36}}{17.6}}{28.5\times 8}}{5\times 5}$$

Express \frac{\frac{5}{36}}{17.6} as a single fraction.

$$\frac{\frac{\frac{5}{36\times 17.6}}{28.5\times 8}}{5\times 5}$$

Multiply 36 and 17.6 to get 633.6.

$$\frac{\frac{\frac{5}{633.6}}{28.5\times 8}}{5\times 5}$$

Expand \frac{5}{633.6} by multiplying both numerator and the denominator by 10.

$$\frac{\frac{\frac{50}{6336}}{28.5\times 8}}{5\times 5}$$

Reduce the fraction \frac{50}{6336} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{\frac{25}{3168}}{28.5\times 8}}{5\times 5}$$

Multiply 28.5 and 8 to get 228.

$$\frac{\frac{\frac{25}{3168}}{228}}{5\times 5}$$

Express \frac{\frac{25}{3168}}{228} as a single fraction.

$$\frac{\frac{25}{3168\times 228}}{5\times 5}$$

Multiply 3168 and 228 to get 722304.

$$\frac{\frac{25}{722304}}{5\times 5}$$

Multiply 5 and 5 to get 25.

$$\frac{\frac{25}{722304}}{25}$$

Express \frac{\frac{25}{722304}}{25} as a single fraction.

$$\frac{25}{722304\times 25}$$

Cancel out 25 in both numerator and denominator.

$$\frac{1}{722304}$$

Factor

$$\frac{1}{11 \cdot 19 \cdot 2 ^ {7} \cdot 3 ^ {3}} = 1.3844586213007266 \times 10^{-6}$$