Solve (9*8/2/5)^3*(5*6/7/63)^5

$$( \frac { \frac { 9 \times 8 } { 2 } } { 5 } ) ^ { 3 } \times ( \frac { \frac { 5 \times 6 } { 7 } } { 63 } ) ^ { 5 }$$

Evaluate

$$\frac{153600}{282475249}\approx 0.000543764$$

Solution Steps

Express \frac{\frac{9\times 8}{2}}{5} as a single fraction.

$$\left(\frac{9\times 8}{2\times 5}\right)^{3}\times \left(\frac{\frac{5\times 6}{7}}{63}\right)^{5}$$

Cancel out 2 in both numerator and denominator.

$$\left(\frac{4\times 9}{5}\right)^{3}\times \left(\frac{\frac{5\times 6}{7}}{63}\right)^{5}$$

Multiply 4 and 9 to get 36.

$$\left(\frac{36}{5}\right)^{3}\times \left(\frac{\frac{5\times 6}{7}}{63}\right)^{5}$$

Calculate \frac{36}{5} to the power of 3 and get \frac{46656}{125}.

$$\frac{46656}{125}\times \left(\frac{\frac{5\times 6}{7}}{63}\right)^{5}$$

Express \frac{\frac{5\times 6}{7}}{63} as a single fraction.

$$\frac{46656}{125}\times \left(\frac{5\times 6}{7\times 63}\right)^{5}$$

Cancel out 3 in both numerator and denominator.

$$\frac{46656}{125}\times \left(\frac{2\times 5}{7\times 21}\right)^{5}$$

Multiply 2 and 5 to get 10.

$$\frac{46656}{125}\times \left(\frac{10}{7\times 21}\right)^{5}$$

Multiply 7 and 21 to get 147.

$$\frac{46656}{125}\times \left(\frac{10}{147}\right)^{5}$$

Calculate \frac{10}{147} to the power of 5 and get \frac{100000}{68641485507}.

$$\frac{46656}{125}\times \frac{100000}{68641485507}$$

Multiply \frac{46656}{125} and \frac{100000}{68641485507} to get \frac{153600}{282475249}.

$$\frac{153600}{282475249}$$

Factor

$$\frac{2 ^ {11} \cdot 3 \cdot 5 ^ {2}}{7 ^ {10}} = 0.0005437644556249245$$