Solve [(-1/2)^{5}*(-1/2)^4]^-1:[(-1)^-3]^2=

$$[ ( - \frac { 1 } { 2 } ) ^ { 5 } \cdot ( - \frac { 1 } { 2 } ) ^ { 4 } ] ^ { - 1 } : [ ( - 1 ) ^ { - 3 } ] ^ { 2 } =$$

Evaluate

$$-512$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 4 to get 9.

$$\frac{\left(\left(-\frac{1}{2}\right)^{9}\right)^{-1}}{\left(\left(-1\right)^{-3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and -1 to get -9.

$$\frac{\left(-\frac{1}{2}\right)^{-9}}{\left(\left(-1\right)^{-3}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply -3 and 2 to get -6.

$$\frac{\left(-\frac{1}{2}\right)^{-9}}{\left(-1\right)^{-6}}$$

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

$$\frac{-512}{\left(-1\right)^{-6}}$$

Calculate -1 to the power of -6 and get 1.

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

Anything divided by one gives itself.

$$-512$$

Factor

$$-512$$