Solve 7div6div5div6div5div4div4div3div3div2

$$7 \div 6 \div 5 \div 6 \div 5 \div 4 \div 4 \div 3 \div 3 \div 2$$

Evaluate

$$\frac{7}{259200}\approx 0.000027006$$

Solution Steps

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5}}{4}}{4}}{3}}{3}}{2} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5}}{4}}{4}}{3}}{3\times 2}$$

Express \frac{\frac{\frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5}}{4}}{4}}{3} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5}}{4}}{4\times 3}}{3\times 2}$$

Express \frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5}}{4} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{\frac{7}{6}}{5}}{6}}{5\times 4}}{4\times 3}}{3\times 2}$$

Express \frac{\frac{\frac{7}{6}}{5}}{6} as a single fraction.

$$\frac{\frac{\frac{\frac{\frac{7}{6}}{5\times 6}}{5\times 4}}{4\times 3}}{3\times 2}$$

Multiply 5 and 6 to get 30.

$$\frac{\frac{\frac{\frac{\frac{7}{6}}{30}}{5\times 4}}{4\times 3}}{3\times 2}$$

Express \frac{\frac{7}{6}}{30} as a single fraction.

$$\frac{\frac{\frac{\frac{7}{6\times 30}}{5\times 4}}{4\times 3}}{3\times 2}$$

Multiply 6 and 30 to get 180.

$$\frac{\frac{\frac{\frac{7}{180}}{5\times 4}}{4\times 3}}{3\times 2}$$

Multiply 5 and 4 to get 20.

$$\frac{\frac{\frac{\frac{7}{180}}{20}}{4\times 3}}{3\times 2}$$

Express \frac{\frac{7}{180}}{20} as a single fraction.

$$\frac{\frac{\frac{7}{180\times 20}}{4\times 3}}{3\times 2}$$

Multiply 180 and 20 to get 3600.

$$\frac{\frac{\frac{7}{3600}}{4\times 3}}{3\times 2}$$

Multiply 4 and 3 to get 12.

$$\frac{\frac{\frac{7}{3600}}{12}}{3\times 2}$$

Express \frac{\frac{7}{3600}}{12} as a single fraction.

$$\frac{\frac{7}{3600\times 12}}{3\times 2}$$

Multiply 3600 and 12 to get 43200.

$$\frac{\frac{7}{43200}}{3\times 2}$$

Multiply 3 and 2 to get 6.

$$\frac{\frac{7}{43200}}{6}$$

Express \frac{\frac{7}{43200}}{6} as a single fraction.

$$\frac{7}{43200\times 6}$$

Multiply 43200 and 6 to get 259200.

$$\frac{7}{259200}$$

Factor

$$\frac{7}{2 ^ {7} \cdot 3 ^ {4} \cdot 5 ^ {2}} = 2.700617283950617 \times 10^{-5}$$