Solve frac{(-27)^{3}(32)^{-5}(-8)^{5}(25^{2})^-6}{(-72)^4(-50^3)^4}

$$\frac { ( - 27 ) ^ { 3 } ( 32 ) ^ { - 5 } ( - 8 ) ^ { 5 } ( 25 ^ { 2 } ) ^ { - 6 } } { ( - 72 ) ^ { 4 } ( - 50 ^ { 3 } ) ^ { 4 } }$$

Evaluate

$$\frac{3}{61035156250000000000000000000000000000000000}=4.9152 \cdot 10^{-44}$$

Solution Steps

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

$$\frac{\left(-27\right)^{3}\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

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

$$\frac{-19683\times 32^{-5}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate 32 to the power of -5 and get \frac{1}{33554432}.

$$\frac{-19683\times \frac{1}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply -19683 and \frac{1}{33554432} to get -\frac{19683}{33554432}.

$$\frac{-\frac{19683}{33554432}\left(-8\right)^{5}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate -8 to the power of 5 and get -32768.

$$\frac{-\frac{19683}{33554432}\left(-32768\right)\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply -\frac{19683}{33554432} and -32768 to get \frac{19683}{1024}.

$$\frac{\frac{19683}{1024}\times 25^{-12}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Calculate 25 to the power of -12 and get \frac{1}{59604644775390625}.

$$\frac{\frac{19683}{1024}\times \frac{1}{59604644775390625}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

Multiply \frac{19683}{1024} and \frac{1}{59604644775390625} to get \frac{19683}{61035156250000000000}.

$$\frac{\frac{19683}{61035156250000000000}}{\left(-72\right)^{4}\left(-50^{3}\right)^{4}}$$

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

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-50^{3}\right)^{4}}$$

Calculate 50 to the power of 3 and get 125000.

$$\frac{\frac{19683}{61035156250000000000}}{26873856\left(-125000\right)^{4}}$$

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

$$\frac{\frac{19683}{61035156250000000000}}{26873856\times 244140625000000000000}$$

Multiply 26873856 and 244140625000000000000 to get 6561000000000000000000000000.

$$\frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000}$$

Express \frac{\frac{19683}{61035156250000000000}}{6561000000000000000000000000} as a single fraction.

$$\frac{19683}{61035156250000000000\times 6561000000000000000000000000}$$

Multiply 61035156250000000000 and 6561000000000000000000000000 to get 400451660156250000000000000000000000000000000000.

$$\frac{19683}{400451660156250000000000000000000000000000000000}$$

Reduce the fraction \frac{19683}{400451660156250000000000000000000000000000000000} to lowest terms by extracting and canceling out 6561.

$$\frac{3}{61035156250000000000000000000000000000000000}$$

Factor

$$\frac{3}{2 ^ {34} \cdot 5 ^ {48}} = 4.9152000000000005 \times 10^{-44}$$