Solve frac{(-7)^{3}*7^{8}*(-45)^2}{7^-4*(-7^3)^5}

$$\frac { ( - 7 ) ^ { 3 } \times 7 ^ { 8 } \times ( - 45 ) ^ { 2 } } { 7 ^ { - 4 } \times ( - 7 ^ { 3 } ) ^ { 5 } }$$

Evaluate

$$2025$$

Solution Steps

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

$$\frac{\left(-45\right)^{2}\left(-7\right)^{3}\times 7^{12}}{\left(-7^{3}\right)^{5}}$$

Calculate -45 to the power of 2 and get 2025.

$$\frac{2025\left(-7\right)^{3}\times 7^{12}}{\left(-7^{3}\right)^{5}}$$

Calculate -7 to the power of 3 and get -343.

$$\frac{2025\left(-343\right)\times 7^{12}}{\left(-7^{3}\right)^{5}}$$

Multiply 2025 and -343 to get -694575.

$$\frac{-694575\times 7^{12}}{\left(-7^{3}\right)^{5}}$$

Calculate 7 to the power of 12 and get 13841287201.

$$\frac{-694575\times 13841287201}{\left(-7^{3}\right)^{5}}$$

Multiply -694575 and 13841287201 to get -9613812057634575.

$$\frac{-9613812057634575}{\left(-7^{3}\right)^{5}}$$

Calculate 7 to the power of 3 and get 343.

$$\frac{-9613812057634575}{\left(-343\right)^{5}}$$

Calculate -343 to the power of 5 and get -4747561509943.

$$\frac{-9613812057634575}{-4747561509943}$$

Divide -9613812057634575 by -4747561509943 to get 2025.

$$2025$$

Factor

$$3^{4}\times 5^{2}$$