Solve frac{2^{7}*3^{8}*5^4}{(3^2)^6*(-2)^4*625}=

$$\frac { 2 ^ { 7 } \cdot 3 ^ { 8 } \cdot 5 ^ { 4 } } { ( 3 ^ { 2 } ) ^ { 6 } \cdot ( - 2 ) ^ { 4 } \cdot 625 } =$$

Evaluate

$$\frac{8}{81}\approx 0.098765432$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{2^{7}\times 3^{8}\times 5^{4}}{3^{12}\left(-2\right)^{4}\times 625}$$

Cancel out 3^{8} in both numerator and denominator.

$$\frac{2^{7}\times 5^{4}}{625\left(-2\right)^{4}\times 3^{4}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{128\times 5^{4}}{625\left(-2\right)^{4}\times 3^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{128\times 625}{625\left(-2\right)^{4}\times 3^{4}}$$

Multiply 128 and 625 to get 80000.

$$\frac{80000}{625\left(-2\right)^{4}\times 3^{4}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{80000}{625\times 16\times 3^{4}}$$

Multiply 625 and 16 to get 10000.

$$\frac{80000}{10000\times 3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{80000}{10000\times 81}$$

Multiply 10000 and 81 to get 810000.

$$\frac{80000}{810000}$$

Reduce the fraction \frac{80000}{810000} to lowest terms by extracting and canceling out 10000.

$$\frac{8}{81}$$

Factor

$$\frac{2 ^ {3}}{3 ^ {4}} = 0.09876543209876543$$