Solve (-2)^7*(-1/2)^-4*(2^-3)^3

$$( - 2 ) ^ { 7 } \cdot ( - \frac { 1 } { 2 } ) ^ { - 4 } \cdot ( 2 ^ { - 3 } ) ^ { 3 }$$

Evaluate

$$-4$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\left(-2\right)^{7}\left(-\frac{1}{2}\right)^{-4}\times 2^{-9}$$

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

$$-128\left(-\frac{1}{2}\right)^{-4}\times 2^{-9}$$

Calculate -\frac{1}{2} to the power of -4 and get 16.

$$-128\times 16\times 2^{-9}$$

Multiply -128 and 16 to get -2048.

$$-2048\times 2^{-9}$$

Calculate 2 to the power of -9 and get \frac{1}{512}.

$$-2048\times \frac{1}{512}$$

Multiply -2048 and \frac{1}{512} to get -4.

$$-4$$

Factor

$$-4$$