Solve frac{(2*3^{2}*5^{3})^4}{(2^4*3^7*5^12)}

$$\frac { ( 2 \cdot 3 ^ { 2 } \cdot 5 ^ { 3 } ) ^ { 4 } } { ( 2 ^ { 4 } \cdot 3 ^ { 7 } \cdot 5 ^ { 12 } ) }$$

Evaluate

$$3$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{\left(2\times 9\times 5^{3}\right)^{4}}{2^{4}\times 3^{7}\times 5^{12}}$$

Multiply 2 and 9 to get 18.

$$\frac{\left(18\times 5^{3}\right)^{4}}{2^{4}\times 3^{7}\times 5^{12}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{\left(18\times 125\right)^{4}}{2^{4}\times 3^{7}\times 5^{12}}$$

Multiply 18 and 125 to get 2250.

$$\frac{2250^{4}}{2^{4}\times 3^{7}\times 5^{12}}$$

Calculate 2250 to the power of 4 and get 25628906250000.

$$\frac{25628906250000}{2^{4}\times 3^{7}\times 5^{12}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{25628906250000}{16\times 3^{7}\times 5^{12}}$$

Calculate 3 to the power of 7 and get 2187.

$$\frac{25628906250000}{16\times 2187\times 5^{12}}$$

Multiply 16 and 2187 to get 34992.

$$\frac{25628906250000}{34992\times 5^{12}}$$

Calculate 5 to the power of 12 and get 244140625.

$$\frac{25628906250000}{34992\times 244140625}$$

Multiply 34992 and 244140625 to get 8542968750000.

$$\frac{25628906250000}{8542968750000}$$

Divide 25628906250000 by 8542968750000 to get 3.

$$3$$

Factor

$$3$$