Solve frac{(-27)^{3}(32)^{-2}(-8)^{4}(25^2)}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 2 } ( - 8 ) ^ { 4 } ( 25 ^ { 2 } ) } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$-\frac{3}{400000000000000000000}=-7.5 \cdot 10^{-21}$$

Solution Steps

Calculate -27 to the power of 3 and get -19683.

$$\frac{-19683\times 32^{-2}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate 32 to the power of -2 and get \frac{1}{1024}.

$$\frac{-19683\times \frac{1}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply -19683 and \frac{1}{1024} to get -\frac{19683}{1024}.

$$\frac{-\frac{19683}{1024}\left(-8\right)^{4}\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate -8 to the power of 4 and get 4096.

$$\frac{-\frac{19683}{1024}\times 4096\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply -\frac{19683}{1024} and 4096 to get -78732.

$$\frac{-78732\times 25^{2}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate 25 to the power of 2 and get 625.

$$\frac{-78732\times 625}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply -78732 and 625 to get -49207500.

$$\frac{-49207500}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate -72 to the power of 4 and get 26873856.

$$\frac{-49207500}{26873856\left(-50^{3}\right)^{4}}$$

Calculate 50 to the power of 3 and get 125000.

$$\frac{-49207500}{26873856\left(-125000\right)^{4}}$$

Calculate -125000 to the power of 4 and get 244140625000000000000.

$$\frac{-49207500}{26873856\times 244140625000000000000}$$

Multiply 26873856 and 244140625000000000000 to get 6561000000000000000000000000.

$$\frac{-49207500}{6561000000000000000000000000}$$

Reduce the fraction \frac{-49207500}{6561000000000000000000000000} to lowest terms by extracting and canceling out 16402500.

$$-\frac{3}{400000000000000000000}$$

Factor

$$-\frac{3}{400000000000000000000} = -7.500000000000002 \times 10^{-21}$$