Solve frac{(-5^{4})^{3}}{10^2[(-2)^2]^3(-15)^4}

$$\frac { ( - 5 ^ { 4 } ) ^ { 3 } } { 10 ^ { 2 } [ ( - 2 ) ^ { 2 } ] ^ { 3 } ( - 15 ) ^ { 4 } }$$

Evaluate

$$-\frac{15625}{20736}\approx -0.753520448$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(-5^{4}\right)^{3}}{10^{2}\left(-2\right)^{6}\left(-15\right)^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{\left(-625\right)^{3}}{10^{2}\left(-2\right)^{6}\left(-15\right)^{4}}$$

Calculate -625 to the power of 3 and get -244140625.

$$\frac{-244140625}{10^{2}\left(-2\right)^{6}\left(-15\right)^{4}}$$

Calculate 10 to the power of 2 and get 100.

$$\frac{-244140625}{100\left(-2\right)^{6}\left(-15\right)^{4}}$$

Calculate -2 to the power of 6 and get 64.

$$\frac{-244140625}{100\times 64\left(-15\right)^{4}}$$

Multiply 100 and 64 to get 6400.

$$\frac{-244140625}{6400\left(-15\right)^{4}}$$

Calculate -15 to the power of 4 and get 50625.

$$\frac{-244140625}{6400\times 50625}$$

Multiply 6400 and 50625 to get 324000000.

$$\frac{-244140625}{324000000}$$

Reduce the fraction \frac{-244140625}{324000000} to lowest terms by extracting and canceling out 15625.

$$-\frac{15625}{20736}$$

Factor

$$-\frac{15625}{20736} = -0.7535204475308642$$