Solve frac{2^{-3}*5^4*-3^8}{15^4*5^-1}

$$\frac { 2 ^ { - 3 } \times 5 ^ { 4 } \times - 3 ^ { 8 } } { 15 ^ { 4 } \times 5 ^ { - 1 } }$$

Evaluate

$$-\frac{405}{8}=-50.625$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\left(-3^{8}\right)\times 2^{-3}\times 5^{5}}{15^{4}}$$

Calculate 3 to the power of 8 and get 6561.

$$\frac{-6561\times 2^{-3}\times 5^{5}}{15^{4}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{-6561\times \frac{1}{8}\times 5^{5}}{15^{4}}$$

Multiply -6561 and \frac{1}{8} to get -\frac{6561}{8}.

$$\frac{-\frac{6561}{8}\times 5^{5}}{15^{4}}$$

Calculate 5 to the power of 5 and get 3125.

$$\frac{-\frac{6561}{8}\times 3125}{15^{4}}$$

Multiply -\frac{6561}{8} and 3125 to get -\frac{20503125}{8}.

$$\frac{-\frac{20503125}{8}}{15^{4}}$$

Calculate 15 to the power of 4 and get 50625.

$$\frac{-\frac{20503125}{8}}{50625}$$

Express \frac{-\frac{20503125}{8}}{50625} as a single fraction.

$$\frac{-20503125}{8\times 50625}$$

Multiply 8 and 50625 to get 405000.

$$\frac{-20503125}{405000}$$

Reduce the fraction \frac{-20503125}{405000} to lowest terms by extracting and canceling out 50625.

$$-\frac{405}{8}$$

Factor

$$-\frac{405}{8} = -50\frac{5}{8} = -50.625$$