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

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

Evaluate

$$\frac{1}{8}=0.125$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{\left(-2\right)^{7}}{\left(-2^{3}\right)^{2}\left(-2^{4}\right)}$$

Calculate -2 to the power of 7 and get -128.

$$\frac{-128}{\left(-2^{3}\right)^{2}\left(-2^{4}\right)}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{-128}{\left(-8\right)^{2}\left(-2^{4}\right)}$$

Calculate -8 to the power of 2 and get 64.

$$\frac{-128}{64\left(-2^{4}\right)}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{-128}{64\left(-16\right)}$$

Multiply 64 and -16 to get -1024.

$$\frac{-128}{-1024}$$

Reduce the fraction \frac{-128}{-1024} to lowest terms by extracting and canceling out -128.

$$\frac{1}{8}$$

Factor

$$\frac{1}{2 ^ {3}} = 0.125$$