Solve frac{(-12)^{4}(-45)^{3}*70^2}{(-60)^3-18^2(-45)^4}

$$\frac { ( - 12 ) ^ { 4 } ( - 45 ) ^ { 3 } \cdot 70 ^ { 2 } } { ( - 60 ) ^ { 3 } - 18 ^ { 2 } ( - 45 ) ^ { 4 } }$$

Evaluate

$$\frac{685843200}{98431}\approx 6967.756093101$$

Solution Steps

Calculate -12 to the power of 4 and get 20736.

$$\frac{20736\left(-45\right)^{3}\times 70^{2}}{\left(-60\right)^{3}-18^{2}\left(-45\right)^{4}}$$

Calculate -45 to the power of 3 and get -91125.

$$\frac{20736\left(-91125\right)\times 70^{2}}{\left(-60\right)^{3}-18^{2}\left(-45\right)^{4}}$$

Multiply 20736 and -91125 to get -1889568000.

$$\frac{-1889568000\times 70^{2}}{\left(-60\right)^{3}-18^{2}\left(-45\right)^{4}}$$

Calculate 70 to the power of 2 and get 4900.

$$\frac{-1889568000\times 4900}{\left(-60\right)^{3}-18^{2}\left(-45\right)^{4}}$$

Multiply -1889568000 and 4900 to get -9258883200000.

$$\frac{-9258883200000}{\left(-60\right)^{3}-18^{2}\left(-45\right)^{4}}$$

Calculate -60 to the power of 3 and get -216000.

$$\frac{-9258883200000}{-216000-18^{2}\left(-45\right)^{4}}$$

Calculate 18 to the power of 2 and get 324.

$$\frac{-9258883200000}{-216000-324\left(-45\right)^{4}}$$

Calculate -45 to the power of 4 and get 4100625.

$$\frac{-9258883200000}{-216000-324\times 4100625}$$

Multiply 324 and 4100625 to get 1328602500.

$$\frac{-9258883200000}{-216000-1328602500}$$

Subtract 1328602500 from -216000 to get -1328818500.

$$\frac{-9258883200000}{-1328818500}$$

Reduce the fraction \frac{-9258883200000}{-1328818500} to lowest terms by extracting and canceling out -13500.

$$\frac{685843200}{98431}$$

Factor

$$\frac{2 ^ {8} \cdot 3 ^ {7} \cdot 5 ^ {2} \cdot 7 ^ {2}}{257 \cdot 383} = 6967\frac{74423}{98431} = 6967.756093100751$$