Solve frac{(-2^{4})^{3}*(-2^3)^4}{(-2)^15*2^6}

$$\frac { ( - 2 ^ { 4 } ) ^ { 3 } \cdot ( - 2 ^ { 3 } ) ^ { 4 } } { ( - 2 ) ^ { 15 } \cdot 2 ^ { 6 } }$$

Evaluate

$$8$$

Solution Steps

Calculate 2 to the power of 4 and get 16.

$$\frac{\left(-16\right)^{3}\left(-2^{3}\right)^{4}}{\left(-2\right)^{15}\times 2^{6}}$$

Calculate -16 to the power of 3 and get -4096.

$$\frac{-4096\left(-2^{3}\right)^{4}}{\left(-2\right)^{15}\times 2^{6}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-4096\left(-8\right)^{4}}{\left(-2\right)^{15}\times 2^{6}}$$

Calculate -8 to the power of 4 and get 4096.

$$\frac{-4096\times 4096}{\left(-2\right)^{15}\times 2^{6}}$$

Multiply -4096 and 4096 to get -16777216.

$$\frac{-16777216}{\left(-2\right)^{15}\times 2^{6}}$$

Calculate -2 to the power of 15 and get -32768.

$$\frac{-16777216}{-32768\times 2^{6}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{-16777216}{-32768\times 64}$$

Multiply -32768 and 64 to get -2097152.

$$\frac{-16777216}{-2097152}$$

Divide -16777216 by -2097152 to get 8.

$$8$$

Factor

$$2^{3}$$