Solve ((-14)^5:7^5)^2*(-2)^3*(-2)

$$( ( - 14 ) ^ { 5 } : 7 ^ { 5 } ) ^ { 2 } \cdot ( - 2 ) ^ { 3 } \cdot ( - 2 )$$

Evaluate

$$16384$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\left(\frac{\left(-14\right)^{5}}{7^{5}}\right)^{2}\left(-2\right)^{4}$$

Calculate -14 to the power of 5 and get -537824.

$$\left(\frac{-537824}{7^{5}}\right)^{2}\left(-2\right)^{4}$$

Calculate 7 to the power of 5 and get 16807.

$$\left(\frac{-537824}{16807}\right)^{2}\left(-2\right)^{4}$$

Divide -537824 by 16807 to get -32.

$$\left(-32\right)^{2}\left(-2\right)^{4}$$

Calculate -32 to the power of 2 and get 1024.

$$1024\left(-2\right)^{4}$$

Calculate -2 to the power of 4 and get 16.

$$1024\times 16$$

Multiply 1024 and 16 to get 16384.

$$16384$$

Factor

$$2^{14}$$