Solve {left({left(-frac{1/2right)}^5{left(-1/2right)}^4right)}^-1}{{left(-1/2right)}^-2}

$$\frac{ { \left( { \left(- \frac{ 1 }{ 2 } \right) }^{ 5 } { \left(- \frac{ 1 }{ 2 } \right) }^{ 4 } \right) }^{ -1 } }{ { \left(- \frac{ 1 }{ 2 } \right) }^{ -2 } }$$

Evaluate

$$-128$$

Solution Steps

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

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

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

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

Rewrite \left(-\frac{1}{2}\right)^{-2} as \left(-\frac{1}{2}\right)^{-9}\left(-\frac{1}{2}\right)^{7}. Cancel out \left(-\frac{1}{2}\right)^{-9} in both numerator and denominator.

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

Calculate -\frac{1}{2} to the power of 7 and get -\frac{1}{128}.

$$\frac{1}{-\frac{1}{128}}$$

Divide 1 by -\frac{1}{128} by multiplying 1 by the reciprocal of -\frac{1}{128}.

$$1\left(-128\right)$$

Multiply 1 and -128 to get -128.

$$-128$$

Factor

$$-128$$