Solve frac{8^{4}*27*(-5)^5}{25^2*9^2*(-4)^5}

$$\frac { 8 ^ { 4 } \cdot 27 \cdot ( - 5 ) ^ { 5 } } { 25 ^ { 2 } \cdot 9 ^ { 2 } \cdot ( - 4 ) ^ { 5 } }$$

Evaluate

$$\frac{20}{3}\approx 6.666666667$$

Solution Steps

Calculate 8 to the power of 4 and get 4096.

$$\frac{4096\times 27\left(-5\right)^{5}}{25^{2}\times 9^{2}\left(-4\right)^{5}}$$

Multiply 4096 and 27 to get 110592.

$$\frac{110592\left(-5\right)^{5}}{25^{2}\times 9^{2}\left(-4\right)^{5}}$$

Calculate -5 to the power of 5 and get -3125.

$$\frac{110592\left(-3125\right)}{25^{2}\times 9^{2}\left(-4\right)^{5}}$$

Multiply 110592 and -3125 to get -345600000.

$$\frac{-345600000}{25^{2}\times 9^{2}\left(-4\right)^{5}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{-345600000}{625\times 9^{2}\left(-4\right)^{5}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{-345600000}{625\times 81\left(-4\right)^{5}}$$

Multiply 625 and 81 to get 50625.

$$\frac{-345600000}{50625\left(-4\right)^{5}}$$

Calculate -4 to the power of 5 and get -1024.

$$\frac{-345600000}{50625\left(-1024\right)}$$

Multiply 50625 and -1024 to get -51840000.

$$\frac{-345600000}{-51840000}$$

Reduce the fraction \frac{-345600000}{-51840000} to lowest terms by extracting and canceling out -17280000.

$$\frac{20}{3}$$

Factor

$$\frac{2 ^ {2} \cdot 5}{3} = 6\frac{2}{3} = 6.666666666666667$$