Solve 16*10^4*3^3/6^5*5^6

$$\frac { 16 \times 10 ^ { 4 } \times 3 ^ { 3 } } { 6 ^ { 5 } \times 5 ^ { 6 } }$$

Evaluate

$$\frac{8}{225}\approx 0.035555556$$

Solution Steps

Calculate 10 to the power of 4 and get 10000.

$$\frac{16\times 10000\times 3^{3}}{6^{5}\times 5^{6}}$$

Multiply 16 and 10000 to get 160000.

$$\frac{160000\times 3^{3}}{6^{5}\times 5^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{160000\times 27}{6^{5}\times 5^{6}}$$

Multiply 160000 and 27 to get 4320000.

$$\frac{4320000}{6^{5}\times 5^{6}}$$

Calculate 6 to the power of 5 and get 7776.

$$\frac{4320000}{7776\times 5^{6}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{4320000}{7776\times 15625}$$

Multiply 7776 and 15625 to get 121500000.

$$\frac{4320000}{121500000}$$

Reduce the fraction \frac{4320000}{121500000} to lowest terms by extracting and canceling out 540000.

$$\frac{8}{225}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {2} \cdot 5 ^ {2}} = 0.035555555555555556$$