Solve frac{15^{4}*18^3}{3^3*5^2*12^2}

$$\frac { 15 ^ { 4 } \times 18 ^ { 3 } } { 3 ^ { 3 } \times 5 ^ { 2 } \times 12 ^ { 2 } }$$

Evaluate

$$\frac{6075}{2}=3037.5$$

Solution Steps

Calculate 15 to the power of 4 and get 50625.

$$\frac{50625\times 18^{3}}{3^{3}\times 5^{2}\times 12^{2}}$$

Calculate 18 to the power of 3 and get 5832.

$$\frac{50625\times 5832}{3^{3}\times 5^{2}\times 12^{2}}$$

Multiply 50625 and 5832 to get 295245000.

$$\frac{295245000}{3^{3}\times 5^{2}\times 12^{2}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{295245000}{27\times 5^{2}\times 12^{2}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{295245000}{27\times 25\times 12^{2}}$$

Multiply 27 and 25 to get 675.

$$\frac{295245000}{675\times 12^{2}}$$

Calculate 12 to the power of 2 and get 144.

$$\frac{295245000}{675\times 144}$$

Multiply 675 and 144 to get 97200.

$$\frac{295245000}{97200}$$

Reduce the fraction \frac{295245000}{97200} to lowest terms by extracting and canceling out 48600.

$$\frac{6075}{2}$$

Factor

$$\frac{3 ^ {5} \cdot 5 ^ {2}}{2} = 3037\frac{1}{2} = 3037.5$$